KR20230172526A - Waveguides and diffraction gratings for augmented or virtual reality displays - Google Patents

Abstract

A waveguide 5002 for use in a virtual reality (VR) or augmented reality (AR) device is disclosed. Waveguide 5002 has an input region 5006 configured to couple light to waveguide 5003 such that the light propagates under total reflection (TIR) within waveguide 5002, and optics configured to receive image bearing light from input region 5006. and an output area 5008 containing the structure. The output area 5008 includes a plurality of regions 5010, 5012, 5014 with different diffraction, and the plurality of regions 5010, 5012, 5014 include diffraction efficiency to reduce rainbow artifacts.

Description

Waveguides and diffraction gratings for augmented or virtual reality displays

The present invention relates to a diffractive waveguide combiner for use in augmented reality or virtual reality displays. In particular, one aspect of the invention relates to a waveguide in which light coupled to the waveguide is not only expanded in two dimensions by a diffractive optical element but also coupled out from the waveguide toward a viewer. This may allow pupil replication, eyebox expansion and relay of projected images in an augmented reality or virtual reality display.

Augmented reality displays provide users, or viewers, with a view of their real-world environment that combines different images, such as images artificially created by a computerized display system. Often overlaid images provide information related to the real world environment. For example, in a transportation application, overlaid images could provide navigation assistance or information regarding hazards. In medical applications, such as in the operating room, overlaid images can provide real-time information about the patient, such as heart rate and blood oxygen levels, or supplementary data to assist the surgeon, such as X-ray images or other medical scans. You can. In video game applications, overlaid images may include computer-generated characters or objects and thus appear to interact with the real world, including viewers, in response to data obtained from other sensors such as cameras. .

In some augmented reality display systems, the overall image presented to the viewer is in the form of a computer-generated display output on a monitor or other visual display screen. In these systems, cameras are used to capture images of the real-world environment and the computer-generated images are then combined and the resulting combination is displayed to the viewer using the hardware and image processing software of a computerized display system. Suitable display systems are widely available and are commonly found in computers, smartphones, tablets, and other devices that combine computational processing, image capture, and visual display screens.

In other augmented reality display systems, the viewer observes the real world directly through transparent or semi-transparent optical devices, often called combiners. The combiner provides a means by which additional images can be overlaid on this real world view. These images are typically produced by a computerized display system coupled to suitable image projection hardware, such as a micro-display based projector.

Providing a direct view of the real-world environment rather than viewing it through image capture and re-display offers a number of advantages, including: field-of-view and resolution of real-world viewing; and dynamic range significantly exceeds the capabilities of currently available artificial display hardware; Eliminating the need to place a display screen in front of the viewer can result in a smaller, more socially acceptable form-factor for the display system; and real-world viewing, including three-dimensional data and focus cues known to be important for long-term wear and eye-fatigue prevention.

Augmented reality display systems that combine additional generated images with a direct view of the real-world environment can be anchored in larger installations, such as the cockpit of an aircraft, in which case they are often referred to as heads-up displays (or HUDs). display devices, or may be fixed to part of a portable device worn by the viewer, in which case they are often referred to as head-mounted displays (HMDs).

A virtual reality display is where the entire image the viewer sees is artificially created. Combiners used in AR-HMDs simply suppress the observation of the real-world, for example by using an opaque black screen between the combiner and the real-world, rather than between the combiner and the viewer's eyes, thereby creating a virtual reality head. It can also be configured for use on a mounted display (VR-HMD).

There are several ways to optically combine computer-generated images with real-world views. A simple method is to make the coupler a piece of partially reflective glass and place it at an angle so that the reflection of the glass allows the viewer to see images outside their field of view. This is an approach used in many autoque systems, where a piece of glass gives the viewer a direct view of the real world by transmitting light from the real world through the glass, as well as a view of text written on the display screen reflected from the glass. to provide. Here, the light reflected from the display screen appears to be overlaid on a view of the real-world environment.

Augmented reality head-mounted displays (AR-HMDs) are advantageous if the display is not too large and cumbersome for the user, especially if long-term wear is expected. This requirement makes the use of a simple, tilted partially reflective screen impractical for anything other than a small field of view for overlaid images.

US4,711,512 relates to an optical device using diffraction gratings and a waveguide of light to realize a combiner for augmented reality displays. In this approach, the coupler consists of a planar slab waveguide made of a suitable light-transmissive material such as glass or plastic. The waveguide is placed in front of the user's eye (or eyes), with a projector provided on one side of the waveguide and out of the user's direct field of view. Light from the projector is scattered from a diffraction grating built into the waveguide or on the surface of the waveguide in the front region of the projector and coupled to the waveguide. The diffraction grating is designed so that the scattered and projected light is reflected completely internally within the waveguide and is generally directed to an area of the waveguide in front of the user's eyes. The light is then scattered off another diffraction grating and coupled out into the waveguide for the user to see. The projector may provide information and/or images that augment the user's real-world view.

The eyebox of an AR-HMD is a measure of the spatial area where the projected image output by the display can be observed with the viewer's eyes. AR-HMDs are often desirable to have an eyebox significantly larger than the eye's pupil size (typically 2-8 mm) to provide a degree of tolerance for the wearing position of the display system. An eyebox that is too small can lead to images that can easily disappear if the viewer's eyes are not in exactly the right position, causing frustration and tension. For direct viewing of the projector, the size of the eyebox is determined by the location of the exit pupil of the projector and the position of the eye relative to the projector. Increasing the eyebox size requires reducing the F-number of the projector, which complicates the design and adds weight and bulk to the overall system, which are all undesirable when a compact form factor must be maintained. Diffractive waveguide combiners (DWCs) may provide an alternative approach to increasing the eyebox size of a display system.

In US 4,711,512, the diffraction grating (hereinafter referred to as output grating) used to output-couple the light of the waveguide is designed to out-couple only a portion of the energy of the incident light beam. Whenever a light beam interacts with the output grating, it is split into at least two beams: an output coupled beam emerging from the waveguide and a beam continuing to propagate within the waveguide. Light remaining in the waveguide, after the distance required to bounce off the surface of the waveguide, interacts with the output grating again, potentially as many times as size allows. In this way, a single input light beam can be output multiple times. If the size of the waveguide cavity is larger than, or can be placed comparable to, the distance between successive interactions with the output grating, the overall output of a beam consisting of multiple overlapping beams is in some way much larger. We will composite the output beam. Therefore, the size of the output beam no longer depends solely on the size of the projector's exit pupil. This phenomenon is referred to as pupil-replication and can be used to output projected light over an extended area of space, providing a larger eyebox than would otherwise be possible. In US 4,711,512, multiple replication of the beam is possible only in the direction of light propagation from the input grating to the waveguide. This limits the expansion of the eyebox to only this direction. Additionally, beams corresponding to different points in the output field of view will expand along slightly different directions. This limits the size of the eyebox that can simultaneously view the entire projected field of view of the display system.

As part of the implementation of a combiner for an augmented reality display, an optical device featuring pupil replication and two-dimensional eyebox expansion is disclosed in WO2016/020643. In WO2016/020543 an input diffractive optical element is provided for coupling light from a projector into propagation of a waveguide within a light-transmissive planar slab substrate. The optical device includes an output number consisting of two diffractive optical elements superimposed on each other, allowing each diffractive optical element to receive light from the input diffractive optical element and combine it towards the other diffractive optical element of the pair. These diffractive elements scatter part of the incident light, keeping it in the waveguide but changing its direction, and scatter part of it depending on the direction of the light beam, allowing it to couple out of the waveguide and be observed. By combining output coupling from a waveguide with diverting the light beam in different directions, diffractive elements provide pupil replication in more than one direction, providing an expansion of the eyebox in two dimensions.

In some embodiments of WO2016/020643, two diffractive optical elements overlaid on each other are provided in a photonic crystal. This can be achieved by an array of pillars disposed on a plane within the waveguide, where the pillars have a different index of refraction compared to the surrounding waveguide medium. Alternatively, the pillars may be configured as a surface relief structure disposed on one of the outer surfaces of the waveguide. In WO2016/020643, the pillars are described as having a ball-to-circular cross-sectional shape in the plane of the waveguide. This arrangement was found to be very effective in expanding the light in two dimensions while simultaneously coupling the light outside the waveguide. Compared to other diffractive couplers, embodiments of WO2016/020643 may provide more efficient use of space in the waveguide, which may reduce manufacturing costs.

An optical device featuring an output element having optical structures having a diamond cross-sectional shape is disclosed in WO2018/178626. A modified diamond cross-sectional shape is also disclosed, wherein the modified diamond features notches cut into two opposing vertices of the diamond profile. Compared to circular structures, optical structures with this modified diamond shape can exhibit a central light strip along the output device with better balanced brightness compared to the rest of the output device. This can reduce undesirable "striping" effects that can occur in the output image, thereby improving the brightness uniformity of the combiner's output.

In the photonic crystal embodiments of WO2016/020643 and WO2018/178626, the diffractive optical features are arranged in a two-dimensional periodic array with hexagonal symmetry. The sum of the two grating vectors associated with this array and the grating vector associated with the one-dimensional input diffractive element is zero. As disclosed in WO2018/178626 and WO2016/020643, this arrangement provides two-dimensional pupil replication and eyebox expansion as well as coupling light outside the waveguide to the viewer.

The modified diamond structure of WO 2018/178626 is effective, but has several drawbacks.

First, there is a need to ensure that the dimensions of the modified diamonds are accurate, including the size of features such as notches. Small deviations in shape from the intended design may result in undesirable scattering characteristics. For example, variations in the shape of a diamond can modify the relative proportions of light coupled into various directions, which can result in a bright central band in the observed image. This creates challenging tolerances in the manufacturing process in which these structures are formed.

Second, the requirement that the shape of the modified diamond structures have dimensions within a narrow range limits the extent to which the optical element can change with position. Instead of modifying the structure to have optimal scattering properties at each location, modified diamond structures must be designed as a compromise between what is required across the entire optical device.

Third, narrow constraints on the morphology of modified diamond structures limit the range of structures that can be optimized according to different considerations. For example, diffractive waveguide couplers receive an input pupil of image bearing light from a projector and then propagate a single input pupil across the output area of the device to achieve various angular positions when the user views the waveguide. It is specifically designed and manufactured to create an eyebox that allows image recognition in; The same diffractive elements can cause unwanted diffraction of external ambient light, such as sunlight or electric lighting, and the external light, which is spectrally broadband for typical light sources, can change its constituent colors due to the dispersive properties of the light scattered by the diffraction grating. By being separated, rainbow artefacts within the eyebox may appear to the wearer of the device as external light. These rainbow artefacts may have the shape of rainbow-colored stripes or bands of light that can appear throughout the user's field of view, thus interfering with the user's view of the intended projected image and/or the real world, thus affecting the user's experience. It can have a negative impact. As a result, what is needed is an improved waveguide that is less susceptible to the appearance of blindness artifacts, at least within the central portion of the eyebox region of the waveguide where the wearer is most likely to observe the projected images. Minimizing these artifacts is desirable in many use cases. However, the scope of what can be achieved with optical structures is limited only if the structures are severely limited in shape and dimensions.

Finally, the optical elements described in both WO2018/178626 and WO2016/020643 are such that the size of the output element is extended so that the two-dimensional extension is diagonal to fill the design eyebox in a direction orthogonal to the direction from the input grid to the output grid. We ask that it be allowed to unfold. This adds the size of the device compared to the minimum size required for a given eyebox.

The purpose of the present invention is to overcome these problems and limitations.

According to one aspect of the present invention, a waveguide is provided for use in a virtual reality (VR) or augmented reality (AR) device, wherein: light is total reflected within the waveguide; an input region configured to couple light to the waveguide to propagate under internal reflection (TIR); and an output region comprising optical structures configured to receive image bearing light from the input region in a direction along a first axis, the output region comprising: A first diffractive interaction, which outcouples light to the viewer, a second diffractive interaction, which outcouples light propagating along a second axis perpendicular to the first axis to the viewer. interaction), and a TIR in the waveguide, including a third diffractive interaction that turns the light to propagate under the TIR in the waveguide along an axis perpendicular to the axis along which it previously propagated. providing a diffraction interaction for light propagating under the light; the output region has a plurality of different non-zero diffraction efficiencies for the first, second, and third diffraction interactions, respectively. comprising a zone, wherein the plurality of zones include: a first zone; and a second zone located at a position along the second axis with respect to the first zone, The diffraction efficiency of the first diffraction interaction in zone 2 is greater than the diffraction efficiency of the second diffraction interaction in the second zone, and is greater than the diffraction efficiency of the first diffraction interaction in the first zone, resulting in a rainbow artifact. or the second diffraction interaction is greater than the diffraction efficiency of the first diffraction interaction in the second zone and is greater than the diffraction efficiency of the second diffraction interaction in the first region, thereby reducing rainbow artifacts.

By having an output area, also called an output grating, the diffraction efficiencies of different areas of the output area having a plurality of different zones can be tailored to be different from each other. It has been found that by having the second zone with this diffraction efficiency configuration, rainbow artifacts from external sources can be reduced as external light is diffracted into the eyebox by the output area. Additionally, having this zone arrangement can help provide improved uniformity of the image in the eyebox. By having this arrangement, the occurrence of such rainbow artifacts can be reduced in the user's field of view.

As used herein, the term zone may be used to refer to a region or section of the output grating that has a specific diffraction efficiency for each diffraction interaction.

The worst case scenario for external light in an output region with a rectangular or square lattice is when the light is incident on the output region along the first or second axis. This is because the diffractive elements in the output area are generally configured to diffract light traveling to the eye in this direction. When using waveguides in a headset, the main source of external lighting comes from above the user's head, from light sources such as the sun outside or lights inside buildings.

When an external light source is incident on the output grating along the second axis, it has a second zone where the diffraction efficiency of the first diffractive interaction is greater compared to the diffraction efficiency of the second diffractive interaction, such that the diffraction when incident on the second zone is The amount of external light is reduced. This means that external light is less likely to cause rainbow artifacts in the eyebox and image. However, the image-bearing light beam coupled to the waveguide through the input region and propagating along the first axis can be coupled in the second zone due to the high efficiency of the first diffractive interaction. Therefore, this region of the output area still contributes to the image delivering light to the eyebox, even though the light primarily travels along a single axis perpendicular to the external light source. Additionally, the diffraction efficiency of the first diffractive interaction in this low rainbow artifact zone is greater than the diffraction efficiency of the first diffractive interaction in the first zone. The relatively high diffraction efficiency of the first diffraction interaction in the low rainbow artifact zone means that the maximum amount of light-bearing images in the second zone is due to the fact that the second and, in some cases, third diffraction efficiencies are low in this zone. This means that outcoupling may occur due to . Compared to the first zone, it is undesirable for the first diffractive interaction to have high efficiency since each of the other diffractive interactions may provide a noticeable contribution in this first zone required to spread the light throughout the grating. . Having this arrangement of zones can help provide eyebox uniformity by reducing rainbow artifacts. This waveguide arrangement can be used in AR devices with side-injection orientation. Specifically, this means that, when used in an AR/VR headset, the input grating injects light into the output grating at a location next to the wearer's eyes (i.e., the first axis is the line that intersects the wearer's left and right eyes). parallel to ). As will be understood, in this orientation external light is incident along the second axis from above the wearer's head.

When an external light source is incident in the first direction, the external light source is diffracted when incident on the second area by having a second zone having a greater diffraction efficiency of the second diffraction interaction compared to the diffraction efficiency of the first diffraction interaction. The amount of light decreases. This means that external light is less likely to cause rainbow artifacts in the eyebox and image. However, an image bearing light beam coupled to the waveguide through the input area and propagating along the second direction can be coupled out of the waveguide towards a viewer in the second area with high efficiency. Therefore, this area still provides image bearing light to the eyebox even though the light travels along a single axis perpendicular to the external light source. Additionally, in this low rainbow artifact region (the diffraction efficiency of the second diffraction interaction in the second zone is greater than the diffraction efficiency of the second diffraction interaction in the first zone), the diffraction efficiency of the second diffraction interaction in the low rainbow artifact second zone Having a relatively high diffraction efficiency means that the maximum amount of image bearing light in the second zone can be outcoupled due to the fact that the first and in some cases third diffraction efficiency is low in this zone. Compared to the zone, it is undesirable for the second diffractive interaction to have a high efficiency since each of the other diffractive interactions may provide a noticeable contribution in this first zone required to spread the light throughout the grating. Having an arrangement of zones can help reduce rainbow artifacts and provide eyebox uniformity.This waveguide arrangement can be used in AR/VR devices with a down-injection orientation. This means that when used in an AR/VR headset, the input grating injects a beam of light into the output grating at a position above the wearer's eyes (i.e., the first axis is perpendicular to the line intersecting the wearer's left and right eyes; The second axis is parallel to the line intersecting the wearer's left and right eyes.) As will be understood, in this orientation external light is incident along the first axis from above the wearer's head.

Preferably, in the second zone, the diffraction efficiency of the first diffraction interaction is: greater than the diffraction efficiency of the second diffraction interaction and the third diffraction interaction in the second zone, or, in the second zone, the diffraction efficiency of the second diffraction interaction is: The diffraction efficiency of the diffractive interaction is greater than that of the first and third diffractive interactions in the second zone.

The first diffractive interaction is not necessarily the first diffractive interaction that light experiences with the output area. For example, light may have experienced a third diffraction interaction before experiencing a first diffraction interaction. This may also be the case for the second diffraction interaction. The first and second diffractive interactions may be referred to as to-eye orders because they couple the image bearing light to the user's eye. The third diffraction interaction can be called a turn order because it causes the direction of light to change. A third diffractive interaction can redirect light traveling along the first axis. For example, the third diffractive interaction may be to divert light ±90° about the first axis. In this way, light that had been propagating along the first axis can experience a third diffractive interaction and then subsequently propagate along the second axis. In another arrangement, the third diffractive interaction can redirect light traveling along the second axis. For example, the third diffractive interaction may be to divert light ±90° about the second axis. In this way, light that had propagated along the second axis can propagate along the first axis after experiencing a third diffraction interaction. In some arrangements, the diffraction efficiency to redirect light traveling along a first axis may be the same as the diffraction efficiency to redirect light traveling along a second axis. In the notation used throughout the detailed description, the Straight to Eye (STE) order may be an example of a first diffraction interaction as it is an outcoupling of light traveling along a first axis. Similarly, the to-eye-after-turn (TEAT) order may be an example of a second diffraction interaction as the TEAT order since it is an outcoupling of light traveling along the second axis.

The image formed in the eyebox arises primarily from light diffracted in the first zone. The first region may be referred to as the “balanced region”. Preferably it has a high efficiency for the third diffraction interaction and a low diffraction efficiency for the first diffraction interaction. As described in WO2016/020643, the transition-orders and the two-eye orders can together provide the functions of pupil replication, eyebox extension and output coupling. Therefore, in the first zone, the diffraction efficiencies of the conversion and two-eye orders, respectively, allow broadening and outcoupling to be balanced in a way that provides uniform output in the formed image.

Preferably, when the second zone has a diffraction efficiency of the first diffractive interaction that is greater than the diffraction efficiency of the first diffractive interaction of the first zone, the second zone may have a diffraction efficiency of the second diffraction interaction that is less than the diffraction efficiency of; or wherein when the second zone has a diffraction efficiency of the second diffractive interaction that is greater than the diffraction efficiency of the first diffractive interaction of the second zone, the second zone has a diffraction efficiency of the first diffractive interaction of the first zone. It may have a diffraction efficiency of the first diffraction interaction that is smaller than the diffraction efficiency. As such, since the diffraction efficiency of the second zone for the second diffraction interaction is lower than that of the first zone, rainbow artifacts caused by external light incident along the second axis can be reduced. Likewise, since the diffraction efficiency of the second zone for the first diffraction interaction is lower than that of the first zone, rainbow artifacts caused by external light incident along the first axis can be reduced.

Preferably, when the second zone has a diffraction efficiency of the first diffractive interaction that is greater than the diffraction efficiency of the second (and optionally third) diffractive interaction of the second zone,

the second zone includes a continuous optical structure along a second axis; or herein, when the second zone has a diffraction efficiency of the second diffractive interaction that is greater than the diffraction efficiency of the first (and optionally third) diffractive interaction of the second zone, the second zone rotates along the first axis. It includes continuous optical structures.

In this way, the second zone may comprise an optical structure that forms a continuous structure along a direction parallel to the direction of light from the external light source. That is, a portion of each optical structure may be coupled to a portion of the next nearest neighboring optical structure along a direction parallel to the direction of light from the external source. In some arrangements, this may form a linear grating along an axis in which the optical structure is continuous. In other arrangements, the grating may not be completely linear along the axis, forming what can be referred to as a pseudo-linear structure. By having this structure, the diffraction efficiency of this region can provide primarily selective diffraction for light traveling along a single axis, which has the advantage of preventing extraneous light from causing rainbow artifacts in the eyebox.

Each zone comprises a first rectangular periodic array of optical structures disposed in a plane defined by a first axis and a second axis, wherein the period of the first rectangular array is defined by the spacing between neighboring optical structures of the first rectangular array -; and a second rectangular periodic array of optical structures disposed in a plane, the period of the second rectangular array being defined by the spacing between neighboring optical structures of the second rectangular array; wherein a first rectangular array of optical structures is superimposed on a second rectangular array of optical structures in a plane such that the arrays are spatially offset from each other in the plane; Here the first array of optical structures is offset from the second array of optical structures by a factor different from half the period of the first or second rectangular array.

This type of grating may be referred to as an interleaved rectangular grating (IRG). Each zone can have an array of optical structures arranged in a repeating pattern, with the optical structures of the first array overlaid on the optical structures of the second array. The two arrays of optical structures are arranged so that the orientations of their rectangular patterns that they form are identical to each other.

The first rectangular periodic array can form a first 2D lattice with rectangular symmetry, and the second rectangular periodic array can form a second 2D lattice with rectangular symmetry.

Advantageously, by using a rectangular lattice the number of possible diffractive interactions is reduced compared to, for example, a hexagonal lattice. A rectangular lattice can have four major diffraction interactions compared to six for a hexagonal lattice. This reduces the number of diffraction interactions that can cause rainbow artifacts in the eyebox. Additionally, using a rectangular lattice can reduce the size of the output grid, as it does not require a pre-expansion area, and also reduces the set of different angles captured in the eyebox, reducing rainbow artifacts.

a first direction, referred to as the y-direction of the grid, which is disposed in the plane parallel to one of the sides of the first rectangular periodic array, and parallel to one of the other sides of the first rectangular periodic array and orthogonal to the first direction. A second direction, referred to as the x-direction of the arranged grid, is defined. The z-direction of a grid can be defined as the direction normal to the plane of the grid. In this way, the x-period can be defined as the separation between the closest pairs of optical structures (i.e., neighboring optical structures) of the first rectangular array, as measured along the x-direction. . The y-period is defined as the separation between the closest pairs of optical structures (i.e., neighboring optical structures) of the first rectangular array, as measured along the y-direction. The second rectangular array has the same It has a cycle. As defined above, the y-direction may be along a first axis and the x-direction may be along a second axis.

The offset may be an x-offset, defined as the separation between a fixed point of one of the optical structures of the first rectangular array and a fixed point of one of the optical structures of the second rectangular array, measured along the x-direction. Alternatively, the offset may be a y-offset, defined as the separation between a fixed point of one of the optical structures of the first rectangular array and a fixed point of one of the optical structures of the second rectangular array, measured along the y-direction. there is. The factor is a first parameter that describes the offset between the first and second rectangular arrays in the x-direction and/or a second parameter that describes the offset between the first and second rectangular arrays in the y-direction. Can contain 2 parameters. In this way, the offset that is different from half a period may be different than half a period in the x-direction and/or half a period in the y-direction.

The offset is preferably measured between the optical structures of the first array and the optical structures of the second array that are closest to each other. The fixed point can be chosen according to convenience, but for simple optical structures it is usually the center of the structure when viewed in the grid plane.

The output area may have a finite range that can be physically implemented. As such, the first and second rectangular periodic arrays may be truncated into a region or set of distinct regions in a plane associated with the grid. Each of these regions defines the shape in which the grid will exist, and although the spatial extent of the first and second periodic arrays may be approximately equal, the offset between the arrays requires that they cannot be cut to exactly the same profile within the plane. This can be explained by the closed profile of interest, but this can be achieved within one period in the x- and y-directions and these will have negligible consequences for the light scattering properties of the grating.

Preferably, when the second zone has a diffraction efficiency of the first diffractive interaction that is greater than the diffraction efficiency of the second (and optionally third) diffractive interaction of the second zone,

The second zone is a structure in which the first array of optical structures differs from the second array of optical structures in the first axis with a period of the first or second rectangular arrangement and the optical structures of the first and second arrays are continuous along the second axis. and an array of first and second optical structures arranged to be offset by a factor different from half the period of the first or second rectangular array, or wherein the second zone is of the second zone. When having a diffraction efficiency of the second diffractive interaction that is greater than the diffraction efficiency of the first (and optionally third) diffractive interaction, the second zone is such that the first optical structure array has a second optical structure in the second axis. from the array by a factor that differs from the period of the first or second rectangular arrangement and differs from half the period of the first or second rectangular array such that the optical structures of the first and second arrays form a continuous structure along the first axis. It may include arrays of first and second optical structures arranged to be offset.

As described above, the second zone may be formed as an optical structure that forms a continuous structure along an axis parallel to the direction in which light from an external light source is incident on the grating. a second rectangular array that is different from both the period of the first or second rectangular array and has an offset that is different from half of the period on an axis perpendicular to the direction in which the external light source is incident on the grating, but such that a continuous structure is formed along said axis; A zone is not simply a linear grid along that axis. However, the diffraction efficiency of the second zone is such that it mainly outcouples light propagating along an axis perpendicular to the direction in which external light is incident on the grating.

In some arrangements, when the second zone has a diffraction efficiency of the first diffractive interaction that is greater than the diffraction efficiency of the first (and optionally third) diffractive interaction of the second zone, the second zone 1 comprising first and second arrays of optical structures, arranged such that the array of optical structures is offset from the array of second optical structures by half the period of the first and second rectangular arrays in the second axis. In other arrangements, this offset in the second axis may be different than half a period but less than the offset in the first axis.

In some arrangements, when the second zone has a diffraction efficiency of the second diffractive interaction that is greater than the diffraction efficiency of the first (and optionally third) diffractive interaction of the second zone, the second zone 1 optical structure array comprising first and second optical structure arrays arranged to be offset from the second optical structure array by half the period of the first and second rectangular arrays in the first axis. In other arrangements, this offset in the first axis may be different than half a period but less than the offset in the second axis.

In some arrangements, the first zone includes optical structures arranged such that the first array of optical structures is offset from the second array of optical structures by a factor that is different from half the period of the first or second rectangular array along the second axis. and the first array of optical structures is offset from the second array of optical structures by half a period of the first or second rectangular array along the first axis.

In this way, by having an offset of the second axis different from half the period of the first or second rectangular arrangement, the diffraction efficiency of the first zone is such that the respective diffraction interaction is present. In some cases, the first zone may have a diffraction efficiency for the third diffractive interaction that is greater than the diffraction efficiency for the first and second diffractive interactions. In the first zone, the diffraction efficiencies of the conversion and two-eye orders, respectively, allow broadening and outcoupling to be balanced in a way that provides uniform output in the formed image.

In another arrangement, the first zone may include a first array of optical structures offset from the second array of optical structures by half the period of the first or second rectangular array along the second axis, wherein the first array of optical structures It is offset along one axis from the second array of optical structures by a factor different from half the period of the first or second rectangular array.

The waveguide may further include a third zone receiving light directly from the input region, the third zone having a third diffraction interaction that is higher than the diffraction efficiency of both the first and second diffraction interactions of the third zone. It has a diffraction efficiency of action; and a third zone is located at a position along the first axis relative to the first zone, the first zone having a diffraction efficiency of the second diffraction interaction that is greater than the diffraction efficiency of the second diffraction interaction of the third zone. .

In this way, the third zone can act as a light diverting area and provide expansion of light throughout the output area. This is because the diffraction efficiency of the third diffractive interaction is higher than that of the first or second diffractive interactions in this region. For example, the third zone may provide expansion along the second axis. Accordingly, light from the input grating may initially expand along the second axis before reaching the first zone. In some arrangements, the third zone also allows light to reach a second zone, which may be located at a position along the second axis from the point where light from the input area initially enters the output area. Because you can. The third zone may also outcouple less light to the viewer than the first zone due to the lower diffraction efficiency of the second diffractive interaction compared to the first zone. This means that more light can reach the first zone, which is responsible for providing light to the largest part of the eyebox.

Preferably, the diffraction efficiency of the first diffractive interaction in the third zone may be less than the diffraction efficiency of the first diffractive interaction in the first zone. This also allows more light to reach the first zone instead of being outcoupled in the third zone upon initial interaction with the output area of the first zone.

If the diffraction efficiency of the first diffractive interaction in the second zone is greater than the diffraction efficiency of the first diffractive interaction in the first zone, the diffraction efficiency of the first diffractive interaction in the second zone is also greater than the diffraction efficiency of the first diffractive interaction in the third zone. It may be greater than the diffraction efficiency of the diffraction interaction, and if the diffraction efficiency of the second diffraction interaction in the second zone is greater than the diffraction efficiency of the second diffraction interaction in the first zone, the diffraction efficiency of the second diffraction interaction in the second zone is greater than the diffraction efficiency of the second diffraction interaction in the second zone. The diffraction efficiency may also be greater than that of the second diffraction interaction in the third zone.

In this way, the low rainbow artifact area can provide the greatest diffraction efficiency for either the first or second diffraction interaction, which is selected depending on the direction of incidence of the external light in the waveguide (along the first or second axis), , which is greater than the diffraction efficiency for the first diffractive interaction or the second diffractive interaction in the first and third zones. Advantageously, by having a high diffraction efficiency for these diffractive interactions, rainbow artifacts from external sources can be reduced for light incident on this part of the output area.

Preferably, the third zone may comprise optical structures arranged such that the first array of optical structures is offset from the second array of optical structures by a factor different from half the period of the first or second rectangular array along the second axis; , the first array of optical structures is offset from the second array of optical structures by half the period of the first or second rectangular array along the first axis.

In this way, the third zone may primarily serve to divert light and may also output a portion of the light.

Preferably, the factor by which the first optical structure array is offset from the second optical structure array along the second axis in the third zone is such that the first optical structure array is offset from the second optical structure array along the second axis in the first zone. It can be smaller than the factor.

In this way, the first and third zones provide different diffraction efficiencies. Advantageously, this means that the third zone can act primarily as a zone of the waveguide diverting the light rather than outcoupling it, compared to the first zone providing a higher proportion of the outcoupling of the light to the viewer.

Alternatively or additionally, the offset in either or both the first and third zones may be along a first axis instead of or in addition to the second axis.

The optical structure of the second section may each have a cross sectional area in a plane defined by the first and second axes that is greater than the cross sectional area of the optical structure of the first section.

For example, the cross-sectional size of the optical structure in the second region may have a size expressed as a ratio to the size of a simple unit cell formed by the first and second optical structure arrays. In some arrangements, the cross-sectional size of the optical structure in the second zone may be 5% of the size of the simple unit cell, which is smaller than the cross-sectional size of the optical structure in the first zone. For example, in some arrangements, the size of the optical structure in the second zone may have a cross-sectional radius of 30% of the unit cell size (i.e., period of the first and/or second axis), wherein the cross-sectional radius is equal to that of the first zone. The size of the optical structure may be 25% of the unit cell size (i.e., period of the first and/or second axis). In other arrangements, the cross-section size may be larger or smaller than this value. For example, the optical structure of the first zone may be a cylindrical structure with a diameter of 0.5p _x (where p _x is the period of the first and/or second rectangular array), and the optical structure of the second zone may be a cylindrical structure with a diameter of 0.5p x . It may be a cylindrical structure with a diameter of p _x .

In some arrangements, the optical structures in the third region may have the same cross-sectional size as the optical structures in the first region. In another arrangement, the optical structure of the third region may have a cross-sectional size that is different from the optical structure of the first region, as well as a cross-sectional size that is different from the optical structure of the second region.

In another arrangement, the optical structures of the second zone may each have a cross-sectional area in a plane defined by the first and second axes equal to the cross-sectional area of the optical structures of the first zone.

For example, the optical structure in the first zone may have a cross-section in the xy plane with a diameter of 0.3-0.7p _x , and the optical structure in the third zone may have a cross-section in the xy-plane with a diameter of 0.3-0.7p _x . and the optical structure of the second zone can have a cross-section in the xy plane with a diameter of 0.3-0.7p _x .

In some arrangements, the optical structure may have a circular cross-section. In this way, the optical structures may be cylindrical pillars. In other arrangements, the optical structure may have a square, rectangular, triangular, parallelogram, or any other shaped cross-section in the waveguide plane. In other arrangements, the optical structure may be a hole relative to the surrounding substrate. For example, they may be cylindrical holes.

The input area may be a one-dimensional linear grid. The input area, or input grating, as it may be otherwise referred to, may couple light to the waveguide and provide light to the first and second arrays of optical structures in a direction along the first axis. The input diffractive optical element is a one-dimensional diffraction grating comprising grooves on one surface of the waveguide and oriented with grooves matching either the x- or y-direction of the interleaved rectangular grating. grating). The input grid may be an input grid as described in WO 2016/020643.

The waveguide may further include a fourth zone disposed at a location along a second axis with respect to the first zone and along the first axis with respect to the second zone, the fourth zone directing light along the first axis toward the second zone. Light is mainly diffracted through third diffraction interactions to selectively convert it.

Advantageously, having a fourth zone increases the efficiency of the output area. The location of the fourth zone means that it can serve to redirect light traveling along the second direction in an area close to the edge of the output area toward the second zone. This prevents light from being lost in the diffraction area, ensuring greater efficiency.

There may be a plurality of fourth zones, one on the first side of the third zone along the second axis and the other on the second side of the third zone along the second axis. Each of the plurality of fourth zones may have a diffraction efficiency that primarily couples light toward the second zone of the output area.

In the fourth region, the offset, which is a factor different from half the period, can be in both the x- and y-directions. In this way, more directional differences between transition orders can be created. This can provide the flexibility to adjust the output element to change the strength of specific transition orders towards the second region.

The waveguide may further include a fifth zone, the fifth zone having the same diffraction efficiency as the second zone, and disposed at a position opposite the first zone relative to the second zone along the second axis.

Area 5 may be an area with a weak rainbow artifact in a similar way to area 2. The second and fifth zones may be located on either side of the first zone. Both the fifth zone and the second zone may provide the same function as each other with respect to diffraction of light.

The period of the optical structures of the first array is preferably constant across the plane of each zone, and the period of the optical structures of the second array is preferably constant across the plane of each zone. This means that the optical structures of both arrays have long-range periodicity across the waveguide in both the x- and y-directions.

The waveguide may also be referred to herein as a diffractive waveguide combiner (DWC). The waveguide may be a planar substrate, such as a planar slab waveguide. The output area, also called the output grating, may be placed within or on the waveguide. For example, it may be located on one of the outer faces of the waveguide. Alternatively, it may be placed within the waveguide provided that the optical structure of the output area is different from the refractive index of the waveguide. The plane of the waveguide may be the same as the plane in which the first and second rectangular arrays are disposed.

The waveguide may comprise: a planar slab of transparent optical material surrounded by a medium having a refractive index lower than that of the planar slab such that light may be confined within the slab by total internal reflection in a direction perpendicular to the planar surface of the slab. . Preferably, the plane of the slab is parallel to the plane of the grid.

The grid need not cover the entire spatial extent of the slab. However, at some specific heats the slab can be made to have a finite spatial extent of at least the size of the grid.

The array of optical structures in the waveguide may be referred to as a one-dimensional or two-dimensional photonic crystal.

According to a further aspect, an augmented reality or virtual reality display comprising a waveguide on the side is provided.

A waveguide may be provided within the optical display. The optical display may be a VR or AR device. This may include VR or AR headsets, head-mounted displays, or heads-up displays.

Preferably, a projector may be provided to project light towards the input area. The projector may be monochromatic or polychromatic and may be provided in an orientation such that the optical axis of the projector lies outside the plane of the waveguide.

As mentioned above, the optical structures can be provided in substantially the same plane in the waveguide. This can be achieved by placing structures on one of the outer surfaces of the waveguide and forming surface relief structures on the grating. Alternatively, structures can be embedded within the waveguide as modifications of refractive index, electrical permittivity, permeability, absorption, and/or birefringence. Both of these are examples of one-dimensional or two-dimensional photonic crystals, depending on whether the structure is periodic in one or two dimensions.

According to a further aspect, a method of manufacturing a waveguide for use in a virtual reality (VR) or augmented reality (AR) device is provided, the device comprising placing an input area within or over the waveguide, and an output area within or over the waveguide. and arranging, wherein the output area has a plurality of zones as outlined in the above aspect.

Note that the term region is used here to convey a sub-region of the output region (i.e., the output diffraction grating). The terms region and sub-region are used interchangeably herein.

As used herein, the term diffraction efficiency may be defined as the radiant power of a particular diffraction interaction relative to the radiant power of an incident beam when incident on that region of the grating.

Embodiments of the present invention will be described by way of example only, with reference to the accompanying drawings below.
1A-1E are a series of diagrams showing the relationship between a lattice of points, a structure and a periodic array of structures, and identification of possible unit cells of the periodic array of structures.
Figure 2 is a top view of a representation of a one-dimensional diffraction grating.
3A-3C show perspective views of some of various one-dimensional diffraction gratings that have different shapes but the same grating vector.
Figures 3D-3F show cross-sectional views in the xz plane of the unit cell of the diffraction grating shown in Figures 3A-3C.
Figures 4A-4F show a series of top views of a diffraction grating showing how a two-dimensional grating can be constructed from the overlap of two one-dimensional gratings to form a two-dimensional lattice, and examples of different two-dimensional gratings having the same basic lattice. do.
5A and 5B show a simplified representation of a projector for an augmented reality or virtual reality display system.
Figure 6 shows a prior art head up display system using a diffractive waveguide coupler.
Figure 7 is a top view of a prior art optical device for expanding an input beam in two orthogonal directions.
Figure 8a shows the grating vectors used to construct a two-dimensional diffraction grating with a rectangular lattice.
Figure 8b shows a top view of a portion of a two-dimensional diffraction grating with a rectangular lattice.
9A is a perspective view of a diffractive waveguide coupler including an output grating according to aspects of the present invention.
Figure 9b is a top view of the same diffractive waveguide coupler as Figure 9a.
9C-9F are perspective views of a diffractive waveguide coupler showing an example path of a light beam through the waveguide.
FIG. 10 shows a cross-sectional view of the diffractive waveguide coupler of FIG. 9A illustrating the generation of multiple output beams from a single input beam.
Figure 11 shows a top view of a portion of an interleaved rectangular grid according to aspects of the present invention.
Figures 12A and 12B show top views of a portion of a perfectly symmetrical interleaved rectangular grid according to aspects of the invention.
Figures 12c and 12d show the identification of alternative lattice vectors in the lattice of a perfectly symmetric interleaved rectangular lattice.
Figures 12E and 12F show top views of profiles of exemplary optical structures for use in embodiments of the invention.
Figure 12G shows a top view of a portion of an interleaved rectangular grid according to an aspect of the invention using the structures shown in Figures 12E-12F.
Figures 12H and 12I show top views of profiles of exemplary multi-element optical structures for use in embodiments of the invention.
Figure 12J shows a top view of a portion of an interleaved rectangular grid according to an aspect of the invention using the structures shown in Figures 12H and 12I.
Figure 13a shows a top view of a portion of an interleaved rectangular grid with a specific arrangement in the x-direction.
Figure 13b shows a top view of a portion of an interleaved rectangular grid with a specific arrangement in the y-direction.
Figure 14a shows a pupil replication map for a diffractive waveguide coupler using a two-dimensional output grating of a prior art device.
Figure 14b shows a pupil replication map for a diffractive waveguide coupler using a two-dimensional output grating according to aspects of the invention.
Figure 15a shows a top view of a portion of an interleaved rectangular grid with individual structures longer than the unit cell of the grid.
Figure 15b shows the unit cell for a periodic structure consisting of individual structures longer than the unit cell.
Figure 15c shows a single structure in which adjacent regions overlap with the same size and shape as the unit cell.
Figure 15d shows a top view of an interleaved rectangular grid with a combined structure to create continuous periodic features.
Figure 15e shows unit cells of the structure to be combined to form continuous periodic features.
Figures 16a-16c show perspective views of the method for lattice geometry.
Figure 16d shows a cross-sectional view of a surface relief grid structure embedded within the medium.
Figure 17a shows a perspective view of modification of the structures introducing a height-dependent slant of the structures.
Figure 17b shows a perspective view of the modification of structures by adding various types of drafts to their sidewalls.
Figure 17c shows a perspective view of modification of the structures introducing a blaze to the top surface of the structures.
Figure 17D shows a perspective view of modification of structures by rounding their edges and/or corners.
Figure 17e shows a top view of the modification of the structures, rounding the cross-sectional profile of the structure, when viewed in the plane of the lattice to which the structures will be connected.
Figure 17f shows a perspective view of modification of the structures introducing an undercut into the structure.
Figure 17g shows a perspective view of modification of structures creating an inverse of the structure.
Figure 17h shows a perspective view of the modification of the structures placing additional small structures on the surfaces of the structure.
Figure 17i shows a top view of an intermediate form of geometric morph applied between two structures with different shaped profiles.
Figures 18A-18D show various methods for adding coatings to an interleaved rectangular grid.
19A and 19B show cross-sectional views of examples of multilayer lattice structures.
Figures 20A-20J show various ways to create differences between periodic structures.
Figure 21A is a perspective view of a diffractive waveguide coupler featuring an interleaved rectangular grating according to aspects of the present invention.
Figure 21b is a top view of the same diffractive waveguide coupler as Figure 21a.
Figure 22a shows a cross-sectional view of a configuration of the present invention using multiple diffractive waveguide couplers.
Figures 22B and 22C show top views of other configurations of the invention using multiple diffractive waveguide couplers.
Figure 23 is a top view of a unit cell of an interleaved rectangular lattice according to the present invention in which one array of optical structures can have a different shape compared to another array of optical structures. .
Figure 24 shows a series of unit cell configurations based on the general definition shown in Figure 23, as well as two transition orders and a two-eye pattern depending on the parameter governing the shape of one side of the structures making up the interleaved rectangular lattice. Shows a graph showing how the diffraction efficiency of each order changes.
Figure 25 shows a series of unit cell configurations based on the general definition shown in Figure 23, as well as two transition orders and a two-eye pattern depending on the parameter governing the shape of one side of the structures making up the interleaved rectangular lattice. A graph is shown showing how the diffraction efficiency of orders changes.
Figure 26 shows a series of heatmaps showing the variation of diffraction efficiency for various diffraction orders with respect to a parameter governing the shape of one of the structures that make up the interleaved rectangular grating.
Figure 27 is a top view of a unit cell of an interleaved rectangular grid according to the present invention showing a shift of one array of optical structures relative to another array of optical structures.
Figures 28a-28c show a series of unit cell configurations and how the diffraction efficiency of the two transition orders varies with angle of incidence for multiple interleaved rectangular gratings with unit cells based on the general definition shown in Figure 27. This is the graph that shows it.
29A-29C show the diffraction efficiency of two transition orders versus angle of incidence for a series of unit cell configurations and multiple interleaved rectangular gratings with unit cells based on the same array of square structures with different shifts between the structures. This is a graph showing how this changes.
Figure 30 is a series of examples corresponding to the invention showing how the diffraction efficiency of the conversion orders and two-eye orders varies with vertical shift of one of the optical structures relative to the other array of optical structures in an interleaved rectangular grating; These are the graphs.
31 is a series of graphs corresponding to examples of the invention showing how the diffraction efficiency of the conversion orders and diffraction orders varies with horizontal shift of one of the optical structures relative to the other array of optical structures in an interleaved rectangular grating. admit.
32 is a series of hits corresponding to examples of the invention showing the variation of the diffraction efficiency of various diffraction orders with respect to the parameters governing the shift of one array of optical structures relative to another array of optical structures in an interleaved rectangular grating. These are maps.
33A-33D are a series of unit cell configurations showing simulation results of the luminance output from a diffractive waveguide coupler with output elements comprised of an interleaved rectangular grid featuring various shifts between arrays of structures in the y-direction; and These are heat maps.
34A-34D show a series of unit cell configurations showing simulation results of the luminance output from a diffractive waveguide coupler with output elements comprised of an interleaved rectangular grid featuring various shifts between arrays of structures in the x-direction; and These are heat maps.
Figure 35a shows a top view of a further configuration of a unit cell according to the invention.
Figure 35b shows a perspective view of a portion of an interleaved rectangular grid based on a periodic array of unit cells according to Figure 35a.
Figure 36 shows a series of heatmaps showing the variation in diffraction efficiency of various diffraction orders for parameters governing the shape of the optical element of Figure 35a.
Figure 37 shows the periodic structure shown in Figure 35b and the periodic structure formed from the unit cell shown in Figure 35a following the opposite modification of the structure.
Figure 38 shows a series of heatmaps showing the change in diffraction order of various diffraction orders for parameters governing the shape of the optical element of Figure 35a upon reverse modification of the structure.
Figures 39A and 39B illustrate a diffractive waveguide coupler featuring a plurality of optical elements according to aspects of the present invention.
Figures 40A-40H show examples of various types of spatial variations for optical elements according to aspects of the present invention.
Figure 41 is a top view of a diffractive waveguide coupler featuring an output grating element with spatial variation in accordance with aspects of the present invention.
Figure 42 is a top view of a diffractive waveguide coupler featuring spatially varying grating elements in accordance with aspects of the invention so that it can be used for both input and output coupling of light.
Figure 43 shows an interpolation scheme that can be applied to the present invention.
Figure 44 shows a top view of geometric morphing methods applied in the present invention.
Figure 45 shows a side view of an exemplary diffractive waveguide coupler showing the optical path between the input grating and the output grating.
Figure 46 shows a side view of an example diffractive waveguide coupler showing the optical path between the input grating and the output grating and showing external light incident on the output grating.
Figure 47 shows a side view of an example diffractive waveguide coupler showing the optical path between the input grating and the output grating and external light incident on the output grating forming a rainbow artifact.
Figure 48 shows a top view of an example diffractive waveguide coupler showing the worst case scenario of external light causing rainbow artifacts in the output image for an output grating with a hexagonal lattice.
Figure 49 shows a top view of an example diffractive waveguide coupler showing the worst case scenario of external light causing rainbow artifacts in the output image for an output grating with a square lattice.
Figure 50 shows a k-space diagram for a diffractive waveguide coupler with an output grating with a hexagonal lattice on which light is incident in the worst case scenario, causing rainbow artifacts in the output image.
Figure 51 shows a k-space diagram for a diffractive waveguide coupler with an output grating with a square lattice on which light is incident in the worst case scenario, causing rainbow artifacts in the output image.
Figure 52 shows a top view of a diffractive waveguide coupler according to the invention with an output grating having a plurality of zones arranged in a lateral injection orientation.
Figure 53 is a top view of a unit cell of an interleaved rectangular grid of the first section of the output grating of Figure 52 according to the present invention showing a shift of one array of optical structures relative to another array of optical structures.
Figure 54 is a graph showing a comparison of the diffraction efficiency of various diffraction interactions versus angle of incidence in a region formed by a rectangular grid interleaved with the unit cell shown in Figure 53.
Figure 55 is a top view of a unit cell of an interleaved rectangular grid of a further zone of the output grating of Figure 52 according to the present invention showing a shift of one array of optical structures relative to another array of optical structures.
Figure 56 is a graph showing a comparison of the diffraction efficiency of various diffraction interactions versus angle of incidence in a region formed by a rectangular grid interleaved with the unit cell shown in Figure 55.
FIG. 57 is an interleaved view of a further zone of the output grating of FIG. 52 according to the present invention showing a shift of one array of optical structures relative to another array of optical structures configured to cause low rainbow artifacts in the output image. This is a top view of the unit cell of a rectangular lattice.
Figure 58 is a graph showing a comparison of the diffraction efficiency of various diffraction interactions versus angle of incidence in a region formed by a rectangular grid interleaved with the unit cell shown in Figure 57.
FIG. 59 is a graph directly comparing how the diffraction efficiency of the TEAT order changes with angle of incidence for the region with the unit cell shown in FIG. 55 compared to the region with the unit cell shown in FIG. 57.
Figure 60 is a top view of the diffractive waveguide coupler shown in Figure 52 showing an example light path through the output grating.
Figure 61 shows a top view of a diffractive waveguide coupler according to the invention with an output grating having a plurality of zones arranged in top-down-injection orientation.
Figure 62 is a top view of a unit cell of a rectangular grid interleaved in the region of the output grating of Figure 61 in accordance with the present invention, showing the shift of one array of optical structures relative to another array configured to cause low rainbow artifacts in the output image; It shows.
FIG. 63 is a graph showing a comparison of the diffraction efficiency of various diffraction interactions versus angle of incidence in a region formed by a rectangular grid interleaved with the unit cell shown in FIG. 62.
Figure 64 is a top view of another diffractive waveguide coupler according to the present invention having an output grating with a plurality of zones arranged in a lateral injection orientation and showing an exemplary optical path through the output grating.
Figure 65 is a top view of a unit cell of an interleaved rectangular grid of a section of the output grating of Figure 64 according to the present invention showing a shift of one array of optical structures relative to another array of optical structures.
Figure 66 is a graph showing a comparison of the diffraction efficiency of various diffraction interactions versus angle of incidence in a region formed by a rectangular grid interleaved with the unit cell shown in Figure 65.
Figure 67 is a top view of a unit cell of an interleaved rectangular grid of a further zone of the output grating of Figure 64 according to the present invention showing a shift of one array of optical structures relative to another array of optical structures.
Figure 68 is a graph showing a comparison of the diffraction efficiency of various diffraction interactions versus angle of incidence in a region formed by a rectangular grid interleaved with the unit cell shown in Figure 67.
Figure 69 is a 2D cumulative order This is a table showing the DWC with the grating period suitable for several qualitatively distinct behaviors of p _x and p _y associated with the beam determined according to .
Figure 70 is a table of various diffraction orders between cumulative order values that may be particularly important for the operation of a DWC.
Figure 71 is a table summarizing the main characteristics of an ideal diffractive waveguide coupler.

It is well known that an array of spatially periodic structures (objects with translational symmetry) can be decomposed into an array of discrete points, called a lattice, at each point where the same structure is placed. Figure 1a shows a portion of a two-dimensional infinite lattice 101 of points with rectangular symmetry. Figure 1b shows a single square structure 102. Figure 1C shows the result of applying an identical copy of structure 102 at each point of lattice 101 to create a periodic rectangular array of structures 103. A unit cell is a selection of a periodic arrangement that, when repeated, places its copies next to each other with the translational symmetry of the lattice, recreating the entire periodic structure. A simple unit cell is the smallest part of the array of periodic structures needed to recreate the array. The unit cell is not unique and can be selected as per convenience. 1D shows one possible unit cell 104 defined to have edges that coincide with the centers of a 2x2 array of optical structures, and with a center that coincides with the center of one of the optical structures. It shows a lattice 103 with other possible unit cells 105 defined as: When repeated at each lattice point, both 103 and 104 produce the same rectangular periodic array. These unit cells are shown again in Figure 1E for clarity.

Systems with spatially periodically varying optical properties, such as periodic arrays of surface relief structures created between media with different refractive indices or periodic arrays of single refractive index structures encapsulated in media with different refractive indices, are characterized by a combination of the direction of light and It is well known that incident light will be scattered in a direction determined by the periodicity and orientation of the lattice relative to its wavelength and periodic array of structures. The intensity of scattering in various directions depends on the wavelength, direction and polarization of the incident light, as well as the type and composition of the changes in optical properties.

When the periodic structure consists of a plane and is used to scatter waves such as electromagnetic waves, it is commonly referred to as a diffraction grating. A periodic structure that follows only one direction is called a one-dimensional diffraction grating, or 1D grating, and a periodic structure in two dimensions is usually called a two-dimensional grating, or 2D grating. Other terms are also used for periodic light scattering structures, such as photonic crystals of various dimensionality. Layered periodic structures are also possible, and when used to scatter electromagnetic waves, they are usually called 1D-, 2D, or 3D-Breg gratings, depending on the dimension of the periodicity, named after physicist Sir Lawrence Bragg. They are referred to as

A diffractive waveguide combiner (DWC) is an optical device that performs a function that can facilitate an augmented reality (AR) or virtual reality (VR) display system using a diffraction grating. When used as part of such a display system, the DWC receives light from an artificial source, which can be a computer-controlled-image-based display system such as a micro-projector, and then determines whether this light will be received by an observer or other sensing system. Light can be output again from a different position of the combiner. In an augmented reality display system, DWC can provide a transmissive viewing of the surrounding physical world. The intended result will be that images from artificial sources will appear to the viewer as superimposed on a view of the surrounding physical world, thus providing an augmented reality display experience. This explanation uses the terms real-world light to refer to light from the surrounding physical world that is seen through transparent viewing through DWC, and DWC to be overlaid on the view of the surrounding physical world. We will use the term projected light to refer to the light from an artificial source that is received.

The present invention relates to a novel configuration of two-dimensional gratings with properties and characteristics suitable for application as output elements of diffractive waveguide couplers (DWC).

Electromagnetic waves and K-space

In theory, any electromagnetic radiation field can be resolved into a superposition of monochromatic plane waves. The electric field of a given plane wave in a linear, isotropic, homogeneous medium with refractive index n can be expressed as a function of position (r) and time (t) as in (1). there is.

(One)

here is a constant vector that describes the amplitude and polarization of the plane wave, is the wave vector of the wave, is the angular frequency of the wave, , and cc mean the complex conjugate of the first part of the expression, so Only real values apply (for simplicity this term is often omitted). The wave vector and each frequency are related to the speed of light c by the dispersion relationship (2).

(2)

In, wave vector The length of is related to the wavelength λ of light in vacuum and the refractive index n of the material through which the wave vector propagates, as shown in (3),

(3)

here,

(4)

am.

For most materials the refractive index n depends on the wavelength in vacuum, but for clarity we do not show this explicitly throughout this description.

Using the Cartesian (x,y,z)-coordinate system for position, we can represent the components of the position as row vectors (5).

(5)

We can also define a Cartesian coordinate system for the wave vector with basis vectors parallel to the Cartesian (x,y,z)-coordinate system of physical space. This vector space is called k-space, and the components of the wave vector can be expressed as a row vector (6).

(6)

If, to describe the direction of the wave vector k, we define spherical angles θ and ϕ, where θ describes the angle between k and the z-direction of the Cartesian coordinate system, and ϕ is the angle of k projected onto the xy-plane. It describes polar coordinates, and therefore the wave vector can be expressed as (7).

(7)

Without loss of generality, but quite conveniently, we can define the plane of the spatial periodic structure to be related to the xy-plane of a three-dimensional Cartesian (x,y,z)-coordinate system. Unless otherwise stated in the remainder of this description, the plane of any spatial periodic structures to be placed in a plane is the xy-, which may be a globally applied coordinate system or a locally defined coordinate system to provide this convenience. It will be assumed to be parallel to the plane. also to the xy-plane (therefore, It is defined as (8) to be a subvector of k in the two-dimensional subspace of k-space parallel to the -plane.

(8)

The wave vector subvectors in this two-dimensional subspace are called xy-wavevectors, and the related subspace of k-space is referred to as k _xy -space. In many situations, the interaction of light with the grating will be in a medium such as a glass waveguide, and the light will undergo refraction to couple to this medium. This refraction can be calculated using Snell's law. Alternatively, as a result of featureless boundary conditions, such as diffraction gratings, at smooth interfaces between different media, the components of the wave vector in the local plane tangent to the interface remain unchanged upon refraction. You can take note. Therefore, if the interface between the media is in the xy-plane in Cartesian (x,y,z)-coordinates, as in most cases described in this document, the xy-wavevector will remain the same upon refraction, which It helps clarify the analysis and allows a more concise representation of the optical phenomenon at play.

No structure realized in the physical world can be truly infinite to the extent that translational symmetry means that it does not extend beyond the edges of a finite periodic configuration. The present invention relates to spatially periodic arrays containing a large number of unit cells, at least millions, if not infinite in extent. The invention also relates to the propagation of light beams smaller than the spatial extent of a lattice. In this way, the scattering process of a light beam in a grating is well approximated by considering an infinite periodic array, and where appropriate, deviations for finite size effects are taken into account.

Waveguide coupling via one-dimensional diffraction grating

It is a well-established principle of optics that light is scattered from a spatial periodic structure in directions characterized by vector equations containing the wave vector components of the light and a vector derived from the lattice associated with the periodic structure. These vectors are referred to as grid vectors. If the lattices are placed in a plane, this equation will only include subvectors within the plane of the lattice.

Figure 2 shows a top view of a one-dimensional diffraction grating 201 placed in the xy-plane. The grid is the distance, which is the period of the grid. It consists of rows of identical characteristics, also called grooves, separated by . In Figure 2, the grating grooves are indicated by a series of lines. The grooves have lines perpendicular to the grooves and at an angle to the x-axis within the xy-plane. It is oriented so that The lines of the grid are described mathematically by (9) through a series of Dirac delta functions δ(x),

(9)

Here, we is expressed as a lattice function associated with the 1D diffraction grating shown in FIG. 2. These functions can be used in the mathematical treatment of the interaction of light with lattice structures, for example through Fourier optics principles and well-established methods. Grid vector associated with grid 201 is defined as a vector in the plane of the grid with a direction perpendicular to the grooves of the grid, and is given as (10).

(10)

As a result of the grid's plane being placed parallel to the xy-plane of the coordinate system, Note that k is a two-dimensional vector in _xy -space.

The diffraction of a monochromatic plane wave from such a grating is given by the 1D grating equation (11):

(12)

here, is a parameter that describes the diffraction order of the interaction and is 0, a positive integer, or a negative integer. here, are respectively and is the xy-wavevector of the incident plane wave with x- and y-direction components given by; Is is the xy-wavevector of the scattered wave corresponding to the diffraction order characterized by , respectively. and With x- and y-direction components given by; and is associated with a 1D diffraction grating. -It is a two-dimensional grid vector on a plane. The interaction of light with a grating characterized by a non-zero diffraction order may be referred to as diffractive interaction. Light beams resulting from interaction with a grating whose diffraction order value is not 0 can be said to be light beams subjected to diffraction interaction.

If a plane wave light beam, also referred to as a collimated light beam, undergoes successive interactions with a given 1D-diffraction grating, each interaction will follow the 1D grating equation. In this situation, relation (13) below shows that after interacting with the same lattice multiple times, the xy-wave vector of the beam must be maintained.

(13)

here, is the xy-wavevector of the original beam before first interacting with the grid, is an integer formed by the sum of all diffraction orders of the previous interactions, where is the lattice vector It is referred to as the cumulative order for the interaction of a light beam with a grating having . For example, a beam undergoes N interactions with the same diffraction grating, If the diffraction order of this ith interaction is, is given as (14).

(14)

Generally, The value of can be 0, positive or negative. Since the light beam corresponding to a specific value of must follow the same dispersion relationship as the incident light, the size of the entire three-dimensional wave vector of the scattered light is given as (15).

(15)

here, is the refractive index of the medium through which the beam propagates. Here, λ is the wavelength of the wave in vacuum, f is the frequency of the wave, and c is the speed of light in vacuum, which all remain constant for a given monochromatic light beam. By noting the definition of the scalar components of the diffracted wavevector, we can relate them to the Cartesian components of the wavevector,

(16)

Expand the equation for the size of the wave vector,

(17)

To solve this, we organize

(18)

and as follows:

(19)

having the same sign as the z-component of the incident beam The values of are referred to as transmitted diffraction orders, while the values at which the z-component of the wavevector changes in sign are referred to as reflected diffraction orders. 0 or complex values of are evanescent orders and correspond to solutions of (39) that do not couple energy or freely propagate light beams.

(20)

These beams are referred to as evanescent orders to refer to the corresponding evanescent electromagnetic waves. These orders do not transport energy without additional structures interacting with other layers of optical structures. For a grating placed at the interface between two media with different refractive indices, the n' values for the transmitted orders may be different from the reflected orders. As a result, other ranges of orders may not be evanescent with respect to the transmitted and reflected diffraction orders.

refractive index refractive index incident on the interface and parallel to the xy-plane in a medium of For light propagating in a medium, the condition under which the beam undergoes total internal reflection (TIR) is the refractive index. The beam in the medium is evanescent. This is given by (21).

(21)

Therefore, the surface parallel to the xy-plane and the refractive index Refractive index placed into the surrounding medium of For a collimated light beam propagating in a system consisting of a planar slab waveguide, three regions of k-space can be identified based on the xy-wavevector of the beam:

One. Free propagation region of k-space - The free propagation region of the k-space-wavevector in this region of k-space is characterized by a light beam that can propagate freely both in the slab waveguide and in the surrounding medium. The wave vector in the free propagation region of k-space satisfies inequality (22).

(22)

2. Waveguided propagation region of k-space - The wavevector in this region of k-space characterizes light beams that can propagate freely within the slab waveguide but not in the surrounding medium, so that such light beams in the waveguide are xy- It undergoes total internal reflection at the interface with the surrounding medium parallel to the plane, where the xy-wave vector remains unchanged. The wave vector in the waveguide region of k-space satisfies inequality (23).

(23)

3. evanescent region of k-space - the wave vector of this region of k-space is characterized by light beams that are evanescent both in the waveguide and in the surrounding medium, and for such light beams some modification of the system is required. Without it, the propagation or transportation of energy is impossible. The wave vector in the evanescent region of k-space satisfies inequality (24).

(24)

The use of diffraction gratings to convert the light beam between the free propagation region of k-space and the waveguide propagation region, while taking into account the limitations imposed by the evanescent region, is the core of the functionality of the DWC.

By taking slabs of index n material on parallel planar sides, it is possible to confine the light beam to a direction orthogonal to the planar surface of the waveguide while allowing propagation of light within the waveguide. This confinement can be used to transport (i.e. relay) a light beam from one location to another within a slim device: the light coming from the projector must satisfy the conditions of the free propagation region and travel through the projector and waveguide. Transmits freely through any medium (usually air); A diffraction grating with appropriate period and orientation in the slab waveguide can be used to diffract light from this projector, satisfying the conditions of waveguide propagation and being confined within the slab by TIR; At a location separate from the first diffraction grating, a second diffraction grating having the same period and orientation as the first diffraction grating is used to diffract some or all of the light beam from the waveguide region into the free propagation region of k-space, where the light beam For this example, it could exit the waveguide towards the observer's eye.

The second diffraction grating may have a different period and orientation than the first diffraction grating, in which case the same inequalities apply to govern the area of k-space. In this case, the xy-wavevector in terms of the initial wavevector and the grating vector interacting with the beam will obtain an additional expression due to the distinct grating vector of the second grating, resulting in (25).

(25)

here, is the grid vector of the second grid, is the cumulative order of interaction with this grid.

Spatially repeating features of a 1D diffraction grating are often referred to as grooves. These grooves can be complex in shape and even composed of various materials. Figures 3a, 3b and 3c all lie in the xy-plane and in the x-direction ( ) and have the same grid period. , but has a different surface relief structure in the z-direction. Each of these cross-sections protrudes in the y-direction to form an array of one-dimensional grooves, to form a complete three-dimensional relief structure.

Figure 3a shows a perspective view of a grating 301 with a two-level surface relief structure. A cross-sectional view of the unit cell of this lattice 304 is shown alone in Figure 3D, consisting of a single protrusion from the surface.

Figure 3b shows a perspective view of a cross-section of a grating 302 with a saw-tooth surface relief structure, where the grating relief consists of ramps inclined along the direction of the grating vector. This lattice structure is also referred to as a blaze structure. A cross-sectional view of the unit cell 305 of this lattice is shown alone in FIG. 3E, and is composed of a single peak with different slopes on each side.

Figure 3C shows a perspective view of grating 303 with a multi-element, multi-level relief structure. A cross-sectional view of unit cell 306 is shown in Figure 3f and is comprised of two separate elements. Despite the presence of separate elements within the unit cell, grating 303 has the same grating vector as gratings 301 and 302.

Because gratings 301, 302, and 303 have the same grating vector, non-evanescent orders of the incident light beam will diffract in the same direction. However, the different shapes of the structures generally mean that, for a given incident beam direction, wavelength and polarization, the propagation of the coupled light in generally non-evanescent transmitted and reflected diffraction orders is different for each of the structures. do.

WAVEGUIDED LIGHT INTERACTIONS WITH TWO-DIMENSIONAL DIFFRACTION GRATINGS

The lattice function (9) can be generalized to provide a method for the mathematical representation of two-dimensional grids in the xy-plane by taking the product of the lattice function for two different one-dimensional grids. 4A shows the grid vectors, respectively. and It shows a schematic diagram of two one-dimensional grids 401 and 402 in the xy-plane with . In row vector form, these grid vectors are given as (26) and (27).

(26)

and

(27)

here, and are the periods of the grids 401 and 402, respectively, and is an angle that describes the orientation of the grid vectors of gratings 401 and 402, respectively (the angle of grating 401 is negative, as depicted in Figure 4A). A function of 2D lattices that arise from the overlap of these lattices, can be expressed as (28), which is the product of a series of direct delta functions.

(28)

Figure 4b shows that 1D grid patterns overlap to form a cross grid structure 403. The product of the delta functions in equation (26) is non-zero only at the points where the grids intersect, leading to an array of points 404, shown with a crossed grid structure in Figure 4C and without a crossed grid structure in Figure 4D. This is a lattice function It is a lattice of a two-dimensional grid described as. The position of each lattice point is a lattice function It can be confirmed through analysis of and is given by (29) and (30).

(29)

and

(30)

here gives the (x,y)-coordinates of the lattice points described by the index values i and j. These exponents may be positive or negative integers, or may be zero.

By associating the same structure, or ensemble of structures, at each point based on these lattices, a diffraction grating for light scattering can be created. These structures must exhibit at least some change in optical properties, such as refractive index, electrical permittivity, permeability, birefringence and/or absorptivity, within the structures or with respect to the medium surrounding the structures. Figures 4E and 4F show plan view representations of periodic arrangements of pillar-shaped structures disposed in the xy-plane with periodicity relative to the lattice 404. Figure 4E shows a top view of an array of rectangular pillar structures 405, and Figure 4F shows a top view of an array of triangular pillar structures 406. As in the case of a one-dimensional grating, the directions in which these or other structures based on the lattice 404 diffract monochromatic planar waves depend on the periodicity and orientation of the lattice but not on the shape of the individual structures. This scattering is governed by the vector form expressed as (31), or

(31)

Or, as in (32), it is governed by the two-dimensional lattice equation, which is the equation of the row-vectors of the scalar components.

(32)

here, { describes the two-dimensional diffraction order of the interaction, where each component can be zero, a positive integer, or a negative integer, is the x-component , and y-component by is the xy-wavevector of the scattered wave corresponding to the two-dimensional diffraction order indexed by . Similar to a one-dimensional grating, after successive interactions with the same 2D diffraction grating, the beam produces a wave vector that satisfies the equation will have

(33)

here, is the xy-wavevector of the original beam before first interacting with the 2D grid, and is an integer formed as the sum of all diffraction orders of previous interactions. where the value set can be referred to as the cumulative order of the 2D lattice. Consider a beam that undergoes multiple diffraction events due to a 2D grating, and for the ith interaction the diffraction order is If we select only a single diffraction beam after each diffraction event, the cumulative order before and after the ith interaction is and has values associated with (34) and (35), respectively.

(34)

and

(35)

if is the cumulative order of the beam after experiencing N interactions with this same diffraction grating, If the two-dimensional diffraction order of the ith interaction with this lattice is, and The values of are given by (36) and (37).

(36)

and

(37)

From these equations, and Since is a positive integer, negative integer, or 0, and It can be clearly seen that the degree is a positive integer, a negative integer, or 0.

The z-component of the complete three-dimensional wave vector can be obtained as (38) from the wave of the light beam in the unchanging vacuum state, the refractive index n' of the medium through which the beam propagates, and the diffracted xy-component of the wave vector.

(38)

As in the case of a one-dimensional grating, it has the same sign as the z-component of the incident beam. The values of are referred to as transmitted diffraction orders, while the values at which the z-component of the wavevector changes in sign are referred to as reflected diffraction orders. 0 or complex values of are evanescent orders and correspond to solutions of (39) that do not couple energy or freely propagate light beams.

(39)

Only transmitted or reflected beams in some orders are likely to be non-evanescent.

Like a 1D grating, the refractive index For a system consisting of a planar slab waveguide of refractive index n arranged with a surface parallel to the xy-plane in the surrounding medium of , three regions of k-space in which different propagation modes are possible can be identified. By interacting with the 2D grid multiple times, The xy-wave vector of the beam leading to the cumulative order of can be expressed as (40).

(40)

here, is the xy-wave vector of the beam before interacting with the 2D grid. The three regions of k-space can be defined as follows:

One. Free propagation region in k-space:

(41)

2. Waveguide propagation region in k-space:

(42)

3. Evanescent region of k-space

(43)

Like 1D gratings, a light beam can undergo a transition between free propagating and guiding regions upon interaction with a suitably configured 2D grating. However, in the case of a 2D grid, and Unless it is on a colinear, the xy-wave vector can be deflected in more than one direction. This additional degree of freedom provides greater capacity for the grating to distribute light spatially within the waveguide. This can be advantageously used to support features such as two-dimensional exit pupil dilation within a DWC.

In a slab-waveguide with a suitably configured 2D diffraction grating, the beam can undergo propagation through the waveguide and interact with the 2D grating in some region of the waveguide. At each interaction the beam may be split into several individual beams corresponding to different diffraction orders of the grating. Some of these beams may remain confined within the waveguide by the TIR and thus interact with the grating again, potentially splitting into multiple beams. This process continues until the various light beams are absorbed, escape the grid region as they are transmitted out of the waveguide medium (allowing for the xy-wavevector in the free propagation region of k-space), and leave the region of the waveguide covered by the grating. It may escape the grating region as it propagates out, and/or be absorbed or escape from the waveguide, for example by hitting sides of the slab waveguide other than the surface parallel to the xy-plane.

After a 2D grid interaction, the direction of the beam depends on the 2D cumulative order of that beam determined up to the most recent grid interaction. Accordingly, this beam will undergo a cumulative order evolution and will therefore trace out a branching path through the waveguide. Several beams derived from the same incident collimated monochromatic beam coupled to the waveguide trace out different paths, although the evolution of the cumulative order is different. Accordingly, accumulation of these beams can provide a spatially extended distribution of input light over a portion of a properly configured waveguide. These paths can be analyzed analytically or by computational methods such as raytracing.

By relating the layout of the two-dimensional periodic structures to the 2D lattice equations, a 2D lattice with defined directional scattering properties can be designed. As in the case of 1D gratings, the proportion of light coupled to a particular grating order depends on the actual structure associated with the grating, as well as the wavelength, direction, and polarization of the incident light.

Diffraction efficiency of diffraction gratings

The term diffraction efficiency will be used to describe the radiant power of a particular diffraction order relative to the radiant power of the incident beam. Here we will distinguish the transmitted and reflected orders from the diffraction grating, since they correspond to different beams, although they have the same xy-wavevector. In mathematical notation, the index value T can be used to indicate whether the beam is of the transmitted or reflected order of the associated grating. Here, the transmission index will be referred to as T, and for the transmitted beam it will be defined as T=1, and for the reflected beam it will be defined as T=-1, so it can be expressed as (44).

(44)

here, are the z-components of the wave vectors of the incident and scattered beams, respectively, is a sign or signum function. If we define

(45)

Equation (45) is converted to the diffraction order and the diffraction efficiency of the beam with transmission index T, the incident wavevector k and the normalized electric vector The diffraction efficiency as a function of is given by (46).

(46)

here,

(47)

(48)

(48) is the diffraction order and is the intensity of the scattered beam with respect to the transmission index T. Since intensity is the radiant power per unit area measured in a plane perpendicular to the direction of propagation, possible changes in the size of the beam due to diffraction must be taken into account and, therefore, is included in equation (49).

(49)

here, is a unit vector in the direction perpendicular to the grid surface, k is the incident wave vector, and is the diffracted wave vector. The intensity of monochromatic plane wave electromagnetic radiation can be calculated from the Poynting vector associated with the electromagnetic wave. In general, the calculation of the scattering properties and diffraction efficiency of the grating takes into account the vector nature of the electromagnetic field and includes polarization effects for both the incident and exit beams.

Various methods for mathematical or computational analysis of the grating design can be used to calculate the scattering of light at various diffraction orders. Analytical calculations can be performed for simple cases and certain approximations. Here, mathematical convolution can be used to describe periodic arrays of finite structures. This method is well established in the field of Fourier optics and is particularly effective for gratings that introduce only small perturbations to the incident wave.

In general, pure analytical methods cannot be used to resolve the optical scattering properties of a grating, but instead numerical techniques such as the finite-difference-time domain method (FDTD) with periodic boundary conditions, or Alternatively, semi-analytical methods such as rigorous coupled-wave analysis (RCWA) should be used. These methods are well established, and extensive literature exists in the public domain describing their use for the analysis of diffraction gratings. Additionally, there are also commercially available (e.g., the Lumerical DEVICE suite from Lumerical Inc) or freely available (e.g., the Meep software package, originally from the Massachusetts Institute of Technology). from the Massachusetts Institute of Technology)) There are several sophisticated software packages that make these techniques readily available to those skilled in the art.

Projectors for augmented reality displays using diffractive waveguide couplers

To understand the operation of a DWC, it is helpful to understand how projected light is configured for use with a DWC. The eyebox is a spatial area that allows viewing of the entire observation field of the projected light output by the DWC. These areas ensure viewing of the output of the DWC over a range of eye movements relative to the DWC, as eye rotation changes the position of the gaze center and changes the wearing position of the display system. It is necessary for The size, shape, and location of the eyebox at a particular distance or range of distances are often design requirements of the DWC. In many cases, the size and shape of the eyebox design are minimums that must be achieved rather than exact requirements.

Many DWCs output the waveguide beam multiple times to expand the size of the eyebox. For such DWC, it may be advantageous for each projected beam to be collimated so that the beam's wavefront is flat. Assuming that the beams are of moderate size and the propagation distance is not too large (e.g., beam diameter > 0.25 mm, propagation distance < 100 mm), the wavefronts of the various beams output from the DWC in this case are, respectively, The propagation distance of the beam may be different, but it will be planar. This means that different outputs derived from the same initial beam appear to occur at the same location as long as they have the same direction. If the beam is not collimated, different outputs derived from the same initial beam may appear to come from slightly different locations due to the evolution of the wavefront between different output events. This can result in artifacts that are undesirable to the viewer, such as reduced image sharpness or a slight shift in the apparent position of portions of the image depending on the position of the viewing eye within the eyebox. To avoid these artifacts, it may be advantageous to ensure that the projected light provided to the DWC is collimated.

Figure 5A is a perspective view of a simple representation of a projector system 501 that can be used to provide projected light to a DWC based augmented reality or virtual reality display. Figure 5b shows a cross-sectional view of the same projector 501. In this system, a source image comprised of a computer-controlled pixel-based image display 502 is collimated by a lens system 503 and directed to an input coupling element of the DWC to provide projected light to an AR or VR display system. Outputs directed light.

Technologies suitable for the display 502 include organic light emitting device based pixel display (OLED display), micro light emitting device based pixel display (μLED), or small cathode-ray tube display. emissive displays such as a CRT display (cathode-ray-tubes display), and a digital micro-mirror device (DMD display, digital-micro-mirror device) or liquid-crystal display (LCOS display) on silicon display)-based reflective displays, etc. For projectors based on reflective displays, additional optical elements not shown in Figure 5A are required to provide incident illumination to the display 502, as well as filtering or redirection of light based on polarization or using total internal reflection. I demand it. The operating principles of various display technologies suitable for providing projected light are well established and widespread; The purpose of the description here is to outline some requirements that may be desirable for an AR or VR display system based on DWC, as well as to provide a mathematical description that may be helpful in explaining the invention.

During operation, each point on the display 502 emits or reflects light toward the lens system 503, creating a collimated beam with a unique direction determined by the point on the display. For example, points 504 and 505 produce collimated beams 506 and 507, respectively, each of which is schematized as three rays in Figure 5A. In this way, the projector translates the pixel position of the display 502 into the direction of the plane wave after the lens 503. Accordingly, light projected from the entire display 502 can be decomposed into an ensemble of plane waves, knowing that this light is associated with a unique point on the display. Typically, the light coming from a display is not monochromatic, so each collimated beam can be further resolved over a range of wavelengths.

To write an equation for the electromagnetic waves emitted by a projector, it is useful to define:

f -> focal length of the imaging system 503 of the projector 501;

W -> half width of image display 502 (total display length in x-direction is 2W);

H -> half height of image display 502 (total display length in y-direction is 2H);

(u,v) -> horizontal (u) and vertical (v) Cartesian coordinates for the position of the display 502, measured within the display plane and the center of the display;

P _D (x,y) -> a function that describes the exit pupil of the projector 502, typically this function has a unified value within the region and is zero everywhere else, the pupil is often circular but does not need to be There is no , and this function could also be a function of (λ,u,v), but is kept here as 0 for simplicity;

E ₀ (λ,u,v) > a function that describes the electric field amplitude generated at the output by the image display position (u,v) at wavelength λ;

k(λ,u,v) Wave vector of the light beam from image display 502 with wavelength λ at position (u,v), collimated by imaging system 503 and output from projector 501.

For example, assuming the projector is in a Cartesian (x,y,z)-coordinate system with the z-axis normal to the plane of display 502, the optical axis of imaging system 503 projects from the center of the display. coincident with the normal, the u- and v-directions of display 502 are parallel to the x- and y-directions of the (x,y,z)-coordinate system. For a projector with a high-quality imaging system that exhibits negligible aberrations and distortions, the wave vector k(λ,u,v) can be expressed in row vector form as (50).

(50)

The output field of view of projector 503 can be found by considering the range of the display and using equation (50). Sometimes, it may be advantageous to refer to the horizontal and vertical viewing angles of the projected light beam. The horizontal angle θ _x is the angle subtended to the z-axis when the beam is projected on the xz-plane, and the vertical angle θ _y is the angle subtended to the z-axis when the beam is projected on the yz-plane. Using this definition, the wave vector of the light beam is given by (51).

(51)

Therefore, we can see (52).

and (52)

The horizontal viewing field of view, _θ

(53)

Similarly, the vertical viewing field of view θ _y is defined as the angle subtended by the extent of the output wavevector when projected onto the yz-plane and is given by (54).

(54)

Electromagnetic field output by the projector 501 observed at the exit pupil can be written as an ensemble of plane waves truncated by the spatial extent of the exit pupil.

(55)

This decomposition does not involve complex arbitrary electromagnetic fields, but instead means that the projector's output can be treated as an ensemble of separate, spatially truncated, monochromatic plane wave components, each of which is simple to analyze. A complete explanation is then provided by the superposition of these components. Moreover, since in many projector systems these components are inconsistent with each other, this superposition can be performed in the intensity domain of the sensed image. By analyzing the propagation of various plane wave components, DWC can be used to understand how to map the output of a projector to an observation device, such as the wearer's eye. Having established this formalism, we can define a collimated light beam as an electromagnetic plane wave with a non-zero wavefront amplitude over a finite area, generally indicated by the exit pupil of the projector. In this way, the projected light of an AR or VR display system is an ensemble of collimated beams, each beam corresponding to a point in the projected image delivered by the display system.

The transformation of a spatially distributed source object into an ensemble of collimated beams, where the direction of a given beam depends on the position of the source object in a manner similar to equation (50), is often referred to as placing the object at infinity, and can be used over very large distances. Similar to having a much larger object, the wavefront from any point source on the object becomes flat when interacting with the system in the hand. An imaging system, such as a camera or an observer's eye configured to receive a collimated beam focused at infinity, produces a sharp point at a location determined by the direction of the incident plane wave. Therefore, an imaging system trained to focus at infinity and observe the ensemble of collimated beams created by optically positioning the object at infinity will produce an image of the original object.

Strictly speaking, since these plane waves have a finite range due to the introduction of the pupil function, diffraction will cause the wave to spread out as it propagates. However, for the purposes of the present invention, the pupil size and propagation distance of interest are such that any diffusion has a negligible effect, except for the general diffraction limited effect on image resolution. Additionally, for analysis based on decomposing the projected light into an ensemble of collimated beams to be valid up to the moment of detection by the eye or image sensor, nonlinear effects with respect to the amplitude of the electromagnetic waves must remain negligible. do. For the wavelength and light intensity ranges commonly used in AR and VR display systems, this condition is well satisfied.

Other image generation devices for use with augmented reality or virtual reality displays using DWC are possible, such as those based on scanning laser beams or using holographic principles. These may be resolved along the lines previously described, but consistent interference effects between different parts of the image and elsewhere may be more important for these systems.

It is often advantageous for projector systems configured for use with a DWC if the exit pupil of the projector's imaging system is located externally, close to or coincident with the input coupling element of the DWC.

Prior art examples of diffractive waveguide couplers

Figure 6 shows a schematic diagram of a head-up display based on DWC described in US 4,711,512. Here the image is formed by a CRT display 601 and collimated by a lens 602, converting the image into an ensemble of collimated beams. The collimated light beams impinge on the waveguide 603 in the area where the 1D diffraction grating 604 is located, called the input grating. The input grating has a pitch and orientation to couple incident light within a target angle range for total internal reflection (TIR) in the waveguide 603 and direct this light to another 1D diffraction grating 605, called the output grating. has The light is confined within the waveguide 603 by total internal reflection until it strikes the output grating 605, at which point some of the light is diffracted at an angle below the threshold of the TIR and toward the observer 606. exits the waveguide.

Figure 7 is a top view of a known waveguide 701 (described in WO2016/020643) that can be used as a diffractive coupler in an augmented reality display system. The described system has an input diffraction grating 702 provided on the surface of the planar slab waveguide 701 for coupling light from a projector (not shown) into the waveguide. Input grid 702 consists of a 1D grid with the grid vector pointing along the X-axis direction. Light coupled to the waveguide travels by total internal reflection toward the output element 703, which includes a two-dimensional photonic crystal 704. In this example, photonic crystal 704 includes pillars (not shown) that have a circular cross-sectional shape in terms of this plan view. The pillars have a different refractive index relative to the refractive index of the surrounding waveguide medium and are arranged in an array with hexagonal symmetry. The hexagonal lattice from which this array is derived has a grid vector at an angle of 60° with respect to the grid vector associated with the input grid. In certain arrangements, the grid vectors of the input grid have the same length as the grid vectors of the output grid. In the coordinate system shown in FIG. 7, the grid vector g ₁ of the input grid is given by (56).

(56)

where p is the period of the input grid and the grid vectors of the output grid is given by (57) and (58).

(57)

and

(58)

From this definition, we note that the sum of the grid vectors of the input grid and the grid vectors of the output grid is 0.

(59)

The result of equation (59) is important for the function of the waveguide when non-monochromatic light is used as the DWC in an augmented reality display. Essentially, this result is the grid vectors and It shows that the cumulative change in the xy-wave vector after the first diffraction is 0. Note that this relationship does not provide any description regarding the z-direction of the light beam. Therefore, the light after such a series of diffraction orders will travel in the same direction as the initial beam before being scattered by these diffraction orders in the xy-plane, and the direction of propagation of the beam in three dimensions will be the same as the initial beam or in the xy-plane. It will be the direction reflected with respect to .

Two-dimensional grid with rectangular lattice

Figure 8a shows two one-dimensional grids. Grid 801 is a one-dimensional grid placed in the xy-plane and has grid vectors aligned parallel to the x-axis, and grid 802 is in the xy-plane with grid vectors parallel to the y-axis of the Cartesian coordinate system. It is a laid out one-dimensional grid. The grid vectors for 801 and 802 are given by equation (60) for grid 801 and equation (61) for grid 802,

(60)

and

(61)

Here, p _x is the period of the grid 801, and p _y is the period of the grid 802.

Figure 8b shows a top view of a two-dimensional lattice 803 with a rectangular orthorhombic lattice. Grid 803 is placed in the xy-plane and has a lattice derived from the overlap of gratings 801 and 802. The dotted lines in FIG. 8B represent the original gratings 801 and 802 and are not intended to imply any physical structure. At each point of the lattice derived from the overlapping gratings 801 and 802, a filler 804 is disposed of a material having a different refractive index from the medium surrounding the grating. In this way, a two-dimensional diffraction grating capable of scattering light is realized. diffraction order In the case of , the relationship between the xy-wave vectors before and after scattering from the grid is respectively and It is expressed as and is given as (62).

(62)

This can be expanded in row vector form to give (63).

(63)

here and am. A diffraction grating constructed using orthogonal grating vectors will be referred to as a rectangular grating.

Figure 9a consists of a planar slab waveguide having a region with an input grating (901) and a region with an output grating (902) arranged with the main optical planes parallel to the xy-plane in the Cartesian (x,y,z) coordinate system. It shows a perspective view of a diffractive waveguide coupler (903) comprised of a light-transmissive substrate (905). The input grating 901 and output grating 902 may each be located on either the front or back side of the waveguide, or may be embedded in a planar surface within the waveguide. The grids do not have to be on the same surface. The output grid 902 is positioned away from the input grid 901. Output grating 902 may be adjacent to input grating 901, or there may be a region between the two gratings without gratings or other optical structures. The output grating 902 may be arranged such that the direction of a line drawn between the center of the input grating 901 and the center of the output grating 902 follows the y-direction of the Cartesian coordinate system associated with the waveguide. FIG. 9B shows a top view of the DWC 903 showing the surfaces of the waveguide substrate 905, input grating 901, and output grating, all of which are parallel to the XY-plane of the Cartesian coordinate system. do.

The micro-projector 904 is arranged to output an optically converted image as an ensemble of collimated beams of light of finite size, which are directed to incident on the input grating 901, in the manner previously described. Typically, the output of micro-projector 904 is part of a computer controlled display system (not shown). As detailed previously, each point in the image for a given wavelength, λ, in vacuum will be associated with a unique wavevector, here denoted by k(λ,u,v), where (u,v) is the micro- These are coordinates that describe the point of the image projected from the projector 904. The xy-wave vector associated with is It is displayed as . The exact parameterization of the coordinates (u,v) is not unique and need not be specified; instead, each pair of coordinates must uniquely describe a point in the image, and thus the direction of the collimated beam from the micro-projector. Paying attention is enough. for your convenience, , We will define a pair of coordinates derived from , where and Since are each function of (u,v), the wave vector of the point is given as (64).

(64)

Like (65) From this point of view, it can be rewritten in a more concise expression.

(65)

The input grating 901 is arranged to point in a direction from the center of the input grating 901 to the center of the output grating 902 and have a grating vector g ₁ given by (66).

(66)

where p ₁ is the period of the input grating, chosen such that after first order diffraction by the input grating 901 the range of collimated output beams from the micro-projector 904 is coupled to the guiding range of the waveguide substrate 905. do. For this purpose, all xy-wavevectors associated with the beam from micro-projector 904 The inequality must be satisfied.

(67)

Here, n ₀ is the refractive index of the medium surrounding the waveguide, and n is the refractive index of the waveguide substrate 905. The definition of allows us to write (68).

(68)

Inequalities for the guiding region of k-space From the perspective of, it can be written as (69).

(69)

In general, both n ₀ and n depend on wavelength, but are not shown explicitly here for clarity.

The output lattice 902 has a rectangular orthorhombic lattice similar to lattice 803 shown in FIG. 8B and is defined to have lattice vectors g _x and g _y given by (70) and (71).

(70)

and

(71)

Note that the periods p _x and p _y of the gratings do not have to be the same. For the purposes of DWC, these periods can have similar magnitudes, such as (72).

(72)

When interacting with the output grid 902, the xy-wavevector is the order of interaction and grid vectors and becomes (73) by, or

(73)

Or, in terms of components, it becomes (74) and (75).

(74)

(75)

In general, multiple interactions with the output grating 902 are possible for waveguided light beams, in which case the xy-wavevector of the beam has the 2D cumulative order Characterized by, (76) is given, or

(76)

Or, in terms of components (77), (78) are given.

(77)

(78)

Here, we see that the x-component of the xy-wavevector depends only on the x-component of the wavevector of the collimated monochromatic beam before coupling to the waveguide, the grating vector _gx and the cumulative order _rx . Similarly, note that the y-component of the xy-wavevector depends only on the waveguide, the grating vectors g ₁ , g _y , and the cumulative order r _y .

If set to , a case specifically related to DWC occurs. In this situation The expression becomes (79).

(79)

Afterwards, by selecting the p _x value that satisfies inequality (80), When this happens, the conditions in the guiding region of k-space can be expressed.

(80)

For DWC with suitable grid periods for p _x and p _y , the 2D cumulative order Accordingly, several qualitatively distinct operations related to the beam can be explained. These are described in Table 1 in Figure 69. The items in Table 1 are generally intended to refer to the direction of the light beam projected on the xy-plane and are therefore independent of the z-direction of the wave vector. Additionally, the general directions described in Table 1 are intended to refer to the dominant component of the xy-wave vector. For example, the general +y direction represents an xy-wave vector with the largest y component and a positive sign. If , these directions are correct. For light beams propagating through a waveguide, the sign of the z-direction of the wave vector is essentially flipped every time the beam is reflected from the surface of the waveguide.

In all cases shown in Table 1 of Figure 69, the z-component of the beam will satisfy relation (81).

(81)

Here, depending on whether the light beam described by the wave vector is in the waveguide substrate 905 or the medium surrounding the waveguide, respectively: or am.

The free-propagation case corresponds to the restoration of the xy-wavevector, which will be equal to its initial value. This case describes a collimated beam that can exit the waveguide, so if the incoming collimated beam is part of the image, so is the outgoing beam. The existence of this case shows the possibility of DWC providing a relay function of light beams from micro-projector 904; The ensemble of collimated beams generated from the micro-projector 904 are all coupled into the waveguide by the input grating 901 and then exit the waveguide again by the cumulative order {0,-1} of the output grating 902; If this ensemble of beams is to be observed by the viewer's eye or an image detector, such as a camera, the image of the micro-projector 904 will be visible to the viewer, thereby completing the relay successfully.

The z-component of the wavevector of the beam with cumulative order {0,-1} will have the same value or the same but opposite sign as the initial beam of the micro-projector 904 when it exits the waveguide. The first case is referred to here as transmission mode output, except that it is noted that the position of the beam would have shifted as a result of waveguide confinement and propagation of the beam between the input grating 901 and the output grating 902. This is because the vector has the same direction as it passes through the waveguide by conventional optical transmission. The case where the sign of k _z is opposite to that of the initial beam of the micro-projector 904 is referred to herein as a reflection mode output, in which case the expected direction of the wavevector reflected from a conventional mirror surface parallel to the xy-plane and It is used similarly. It should again be noted that the position of the beam will shift due to waveguided confinement and propagation between the input grating 901 and the output grating 902. Like other diffraction orders, the diffraction intensity in either transmission or reflected output mode depends on the wavelength, direction and polarization of the incident beam, as well as the structure and composition of the grating.

and In principle, according to Other values of are possible, but in many practical cases (82) will be evanescent beams.

or (82)

Except for the various other cases above, and Some combinations of may result in evanescent waves. When this occurs, it means that propagation along the path requires the use of these 2D cumulative degree values. and This means that such values of should be prohibited. especially, or here in case of, and Some values of may result in free propagation of the wave. In this case, this provides an additional mechanism for output from the DWC, but is generally undesirable as it usually causes image artifacts. This problem can be suppressed by choosing grating periods that ensure that the light beam produced by these propagation modes is very weak and/or lies outside the eyebox of the DWC.

In addition to the 2D cumulative orders mentioned in Table 1 of Figure 69, it is helpful to note the various diffraction orders between cumulative order values, which may be particularly important to the operation of the DWC. These orders are listed in Table 2 in Figure 70. As shown in Table 1, the directions refer to the direction of the beams in the xy-plane and ignore the z-component of the wave vector.

As previously mentioned, the diffraction efficiency for coupling between non-evanescent orders will generally depend on the structure and configuration of the grating as well as the wavelength, direction and polarization of the incident light beam.

The diffraction orders specified in Table 2 of FIG. 70 are largely divided into two-eye orders (STE, TEAT+X. TEAT-X, TEAT-Y) or transition orders (T+X, TX, BT-Y, BT-X, It can be classified as BT+X, TTB+X, TTB-X). In particular, for two-eye orders, the sum of the order values m _x and m _y is given by (83), while

(83)

For transition orders, the sum of the order values is given by (84).

(84)

Another important diffraction order is the zero-order interaction. am. This order corresponds to the case where the xy-wavevector does not change, so the beam confined by the TIR within the waveguide remains confined, and the beam propagating freely through the waveguide remains free to propagate (at the waveguide surface (although it can be reflected from). This is important for both projected light beams delivered within the DWC, as well as real-world light beams. Generally, in augmented reality applications it is desirable for real-world light to be directed to an observer through a waveguide. It is the zero-order interaction with the grid that primarily allows this transparent viewing. In many AR applications, it is desirable to make the viewing of the surrounding physical world as bright as possible, which means that the transmission efficiency of real-world light is as high as possible. This requires that the zero-order diffraction efficiency be as close to unity as possible for the angle of incidence corresponding to the light beam corresponding to the free propagation region of k-space. Note that the direction of the light beam relative to real-world light is necessarily different from the waveguide direction of the projected light. Accordingly, in some systems, it may be advantageous to use diffractive structures that provide scattering properties that are particularly dependent on whether the light beam is in the relevant directional range of waveguide projection light or is freely propagating real-world light.

Various accumulation orders {r _x ,r _y } and diffraction orders _{{ m} provides. Typically, each interaction with the output grating 902 generates several new beams, since multiple diffraction orders occur simultaneously, each of which produces a new beam with a different cumulative order {r _x , r _y } in a different direction. This results in a move to . The number of beam paths through which light beams can pass through the waveguide tends to increase exponentially with the number of interactions with the output grating 902.

9C-9F show perspective views of an example number of paths for multiple light beams passing through DWC 903. Here the paths are represented as ray lines (rays) pointing in the direction of the wave vector of the corresponding collimated light beam. All paths start with the same ray 906 at the micro-projector 904 that strikes the input grating 901 and couples to a ray 907 that propagates generally in the +y direction. Therefore, Ray 907 corresponds to cumulative order {0,0}. For clarity, the bounce of rays between the surfaces of the DWC due to waveguide propagation leading to a zigzag path is not shown in the figure. Typically, when a beam propagates through a waveguide, many bounces occur between the waveguide surfaces, and bounces that do not change the direction of the beam correspond to zero-order diffraction with the output grating 902, leaving the xy-wavevector unchanged. means.

FIG. 9C shows the path that beam 907 undergoes propagating in the waveguide until it reaches point 909 where the beam is coupled to the outside of the waveguide through a reflection mode of order STE along path 908 and is directed toward observer 919. shows.

Figure 9D shows the path that beam 907 takes through waveguide propagation until it reaches point 911 where it is steered in the general +x direction by order T+X. The beam is then coupled out of the waveguide via a reflection mode of order TEAT+X along path 910 and undergoes waveguide propagation until it reaches observer 919.

Figure 9E shows a path similar to that of Figure 9D, except that at point 911 the beam is steered generally in the -x direction by order T-X. After propagating into the waveguide to point 914, the beam is coupled out of the waveguide via a mode of order TEAT-X along path 913 and directed toward observer 919.

Figure 9F shows the path that beam 907 takes through waveguide propagation until it reaches point 916 where the beam steers in the general -x direction by order T-X. The beam then undergoes waveguide propagation until it reaches point 917 where it reorients in the general -y direction by order TTB-X. The beam then couples out of the waveguide via a reflection mode of order TEAT-Y along path 915 and undergoes waveguide propagation until it reaches point 918 facing observer 919.

The relay function of the DWC is provided by the spatial separation of the input grid 901 from the output grid 902, according to the example shown in Figures 9a-9f. The requirement that the light beams travel between different regions of the waveguide 903 is such that when the beam is coupled out of the waveguide 903 by the output grating 902, it is at a spatially separate location from the input grating 901. It is absolutely required that there be.

The pupil expansion function of the DWC is provided by multiple paths that may be output at different positions but in the same direction and may have the same xy-wave vector as the input beam, as shown in the examples in FIGS. 9A to 9F. For this pupil expansion to be effectively achieved, it is important that the distance between interactions with the output grating 902 is kept short enough so that the separate output beams are close together or overlap with each other. This will ensure that the pupil of the observer 919 overlaps at least one output beam, which is a necessary condition to enable observation.

given cumulative order and the distance between the interactions with the output grating 902 on the surface of the waveguide 903, which is determined according to the thickness t of the waveguide. is (85).

(85)

Initial wavevector direction parameters In terms of , equation (85) can be written as (86).

(86)

The size of each output beam depends on the overlap of the beams of the input grating 901 and the micro-projector 904. Typically, the input grating 901 will be of sufficient size and shape to accommodate all beams of the micro-projector 904 within the grating. In this case, the size of the output beams will be determined by the beams of the micro-projector 904.

Assuming that good overlap with the input grating 901 is achieved, to achieve good pupil dilation it is generally It is desirable to ensure that is projected onto the xy-plane of the input grid 901 and and The wavelength λ and direction from the micro-projector 904 measured in the direction of the xy-wavelength vector corresponding to is the width of the beam corresponding to . In many projector designs, the value will be the diameter of the circular exit pupil.

Figure 10 shows a cross-sectional view of the diffractive waveguide coupler 903. A collimated ray from a micro projector (not shown), shown in FIG. 10 as ray 1001, is incident on the input grating 901 of the DWC 903 and coupled to the waveguide propagation. This beam propagates in the general +y direction toward the output grating 902, where it splits into several, branching paths. Some of these paths lead to output beams represented by rays 1002, 1003, 1004, 1005, and 1006, shown by way of example. The output beams are directed to a detector 1007, which can be a camera, an observer's eye, or another optical sensing system. Detector 1007 has a limiting aperture 1008 (also referred to as an entrance pupil) that blocks some or all of the output beams 1002, 1003, 1004, 1005, 1006. For clarity, the aperture 1008 is shown as separate from the detector 1007, but in practice this aperture would typically be internal to the detector, for example, the pupil of a human eye or the aperture stop of a camera lens. will be. The portion of the beams that pass through the aperture 1008 essentially constitutes a new beam 1009, herein referred to as the detected beam. Typically, each input beam to a DWC is associated with a corresponding detected beam, derived from the intersection of the ensemble of output beams and the detector aperture used to observe the output of the DWC.

Characteristics of an ideal diffractive waveguide coupler

Generally, a diffractive waveguide coupler uses diffraction gratings to couple light into a waveguide, spatially distributing the light across a portion of the waveguide through multiple branching paths, and coupling at least a portion of the light back toward an observer or other detector. It functions by doing. These main functions are described at length and include input coupling (to describe the conversion of incident light into waveguide propagation), output coupling (to account for the conversion of waveguide light into free propagating light traveling outside the waveguide), and relays. (to account for the transport of light from one spatial region to another), and eyebox expansion (generating multiple overlapping beams from a single input beam to expand the size of the spatial region available for viewing relative to the input). (to explain what is done).

It is helpful to clarify some of the characteristics required for DWC to be performed effectively. Some of the key characteristics of an ideal diffractive waveguide coupler are summarized in Table 3 in Figure 71.

In practice, it is impossible to meet the ideal requirements of a DWC simultaneously, and as limited by design and manufacturing limitations, practical realization will be a balanced compromise depending on the relative importance of various characteristics for the task at hand.

As previously mentioned, the many paths a light beam can take through a DWC will occur with relative intensities depending on the wavelength, direction and polarization of the light beams, as well as the structure and composition of the grating. For output gratings based on rectangular orhohombic lattices, it has been found difficult to achieve good uniformity across the eye box. In particular, a portion of the eyebox output of the light beams may occur primarily through the STE order, while other parts of the eyebox may have light beams that have undergone at least one T+X or T-X transition order to reach the required location within the waveguide. It is required. These beams are then followed by TEAT to-eye orders for outputting the beam. The large difference in the combining efficiency of the transition orders and TEAT to-eye orders compared to the STE order causes non-uniformities in the observed image with respect to the viewing angle of the image and/or the viewer's eye in the eyebox.

Definition of INTERLEAVED RECTANGULAR GRATING (IRG)

The interleaved rectangular grating (IRG) introduced as the subject of the present invention provides a new method for the design and control of the diffraction efficiency of different diffraction orders of rectangular gratings. This additional control can help provide superior performance for diffractive optical elements in applications such as those used as output gratings for diffractive waveguide couplers.

An interleaved rectangular grid can be defined as:

i) two arrays of periodic rectangular structures, periodic structure (PS1) and periodic structure (PS2), are each defined to have a rectangular orthorhombic lattice disposed in the same plane; For convenience, without loss of generality, and unless otherwise stated, this plane is defined as the xy-plane in the Cartesian (x,y,z)-coordinate system; This coordinate system may be a locally defined coordinate system created purely for the purpose of describing the grid itself, or it may be a global coordinate reference to a larger system.

ii) the lattice L1 of the periodic structure PS1 and the lattice L2 of the periodic structure PS2 are both composed of lattice vectors g _x and g _y in the plane of the periodic structures PS1, PS2; g _x and g _y are orthogonal to each other.

iii) the IRG unit cell has a rectangular shape lying in the plane of the periodic structures (PS1, PS2); A pair of sides of the IRG unit cell are parallel to the lattice vector g _x and have a length equal to the period associated with the lattice vector g _x ; The other pair of sides of the IRG unit cell are parallel to the lattice vector g _y and have a length equal to the period associated with the lattice vector g_y; The position of the IRG unit cell is not defined within the xy-plane and may be chosen for convenience.

iv) Within the plane of the periodic structures (PS1, PS2), the lattice (L2) is offset in position from the lattice (L1) by a vector lying in the plane of the periodic structure, the lattice offset vector It is referred to as; The lattice offset vector provides the offset of the lattice (L2) in both the x-direction and y-direction.

v) At each point of the lattice (L1) an identical structure (S1) is associated, which structure is finite in extent and can be composed of several materials, so that a periodic structure (PS1) is associated with each point of the lattice (L1). It is created by placing an identical copy of the structure (S1) in .

vi) At each point of the lattice (L2) an identical structure (S2) is associated, which structure is finite in extent and can be composed of several materials, and therefore a periodic structure (PS2) is associated with each point of the lattice (L2). It is created by placing an identical copy of the structure (S2) in .

vii) An interleaved rectangular grid may be created by combining the periodic structures PS1, PS2 in substantially the same plane and then placed on the surface of the substrate or embedded within the substrate.

For convenience, and unless otherwise specified, certain embodiments of the interleaved rectangular lattice described in this document are based on the definitions described in i) to vii) above, and include a set of structures (S1, S2), a lattice s (L1, L2), lattice vectors (g_2, g_3), lattice offset vector (o_xy), periodic structure (PS1) formed from lattice (L1) and structure (S1), from lattice (L2) and structure (S2). It will be associated with the formed periodic structure (PS2), and the IRG unit cell. Additional modifications and variations of the IRG may be possible and such changes will be explicitly described in the following description.

The term structure here is meant to imply any kind of change in physical properties with respect to position. For example, the term may refer to the geometry of a material with different refractive indices, or it may refer to changes in optical properties within a single material, such as changes in the alignment of liquid crystal molecules, resulting in spatial changes in birefringence. Additionally, the term 'structure' may refer to one or more materials or strain types, and thus the structures (S1, S2) may be composed as a complex of multiple sub-structures, which may be separated or combined with each other and may be composed of different materials.

In some arrangements, structure S1 and/or structure S2 are made of materials that have different optical properties relative to the medium surrounding the combined structure. These differences in optical properties include, but are not limited to, refractive index, electrical permittivity, permeability, birefringence and/or absorption. In general, structures featuring changes in these optical properties can serve as two-dimensional diffraction gratings for the scattering of light, including those used as diffraction grating elements in diffractive waveguide couplers.

If the periodic structures (PS1, PS2) are spatially separated so that they do not overlap each other, they can be directly superimposed on the plane to form the IRG. However, when structures overlap, some combination principle must be applied. For example, a geometric union can be envisioned where the overlap areas between PS1 and PS2 are merged in space. If PS1 and PS2 have different overlapping optical properties, rules can be used to dictate the combined result. For example, if there is a change in refractive index, the rules could favor the index of one structure over another, take the average, take the maximum/minimum value, or take a third value. In some cases, the combination may be determined by manufacturing methods.

All structures realized in the real world must have some thickness in the direction perpendicular to the plane of the IRG. IRGs for scattering light for use in DWC will typically have a thickness ranging from 1 nm to 10000 nm, or 10 nm to 2000 nm, or 20 nm to 500 nm.

Figure 11 shows a top view of a cross section of an exemplary interleaved rectangular grid (IRG) 1101 in accordance with the present invention. IRG 1101 is composed of a superimposition of a periodic structure (PS1) and a periodic structure (PS2). In FIG. 11, the points of the lattice L1 where the periodic structure PS1 is formed are indicated by dots 1102, and the points of the lattice L2 where the periodic structure PS2 is formed are indicated by crosses 1103. ) is displayed. Dots 1102 and crosses 1103 are not intended to convey physical structure. _The lattice vectors _g For convenience and without loss of generality, we define a local Cartesian (x,y,z)-coordinate system so that these lattice vectors are aligned to the x- and y-axes of the coordinate system so that the lattices are placed in the xy-plane of the new coordinate system. You can. Therefore, the grid vectors can be written as (87) and (88).

(87)

and

(88)

The lattice (L2) is located in the same plane as the lattice (L1), but there is an offset in position. Since the lattice is placed in a plane, this position offset can be specified by a two-dimensional vector called the lattice offset vector o _xy , with components describing the position offset in the x- and y-directions.

(89)

_{where o} The (x,y)-coordinates of the points of lattices L1 and L2 are obtained from equations (29) and (30), using the expressions for the lattice vectors given in (87) and (88),

(90)

Regarding the location of the lattice L1 point, , indexed and , and

(91)

Regarding the location of the lattice L2 point, As indexed by and . The indices i and j are used to calculate the lattice position and can be positive or negative integers, or 0. The coordinates (x ₀ , y ₀ ) define the origin of the lattice. Since we can redefine the origin of the Cartesian coordinate system to suit our convenience, for clarity we will set this coordinate to (0,0) and ignore including these terms for the remainder of this description unless otherwise noted. do.

In this example, the form of structure S1 is a pillar with a circular cross-section 1104, and the form of structure S2 is a pillar with a triangular cross-section 1105.

Since the lattices of each periodic structure that makes up the IRG have the same periodicity as those that also contain the IRG, we expect the diffraction orders of the IRG to match those of the rectangular lattice given by equation (62). When using the IRG 1101 as the output grating 902 in the diffractive waveguide coupler 901 shown in FIG. 9A, the nomenclature for the diffraction orders shown in Table 2 in FIG. 70 is adopted and Table 1 in FIG. 69 is adopted. One may note the specific cumulative order presented in . As with other diffraction gratings, the efficiency of various diffraction orders for a given incident beam depends on the shape and configuration of the structures, the layout of the grating, its orientation, and the polarization of the incident beam.

Diffraction scattering properties of interleaved rectangular gratings

Here, a specific type of fully symmetric interleaved rectangular grating (FSIRG) is defined as an interleaved rectangular grid that satisfies the following additional constraints:

i) The structure (S1) and structure (S2) of FSIRG have the same shape, composition, and optical properties,

ii) ii) The lattice offset vector 92 is chosen such that the points of the lattice L2 lie midway between the points of the lattice L1 in both the x- and y-directions.

(92)

FIG. 12A shows FSIRG 1201 where structures S1 and S2 are columns with circular cross-section 1204. Points of the lattice L1 of the FSIRG 1201 are indicated by dots 1202, and points of the lattice L2 are indicated by crosses 1203 (dots and points ( points are for clarity and do not indicate physical differences). The lattices are placed so that the lattice vectors are given by equations (87) and (88). The (x,y)-coordinates of the points of the lattice L1, indexed by i and j, are (93),

(93)

and the (x,y)-coordinates of the points of the lattice L2, indexed by j, are (94).

(94)

Figure 12b shows the same perfectly symmetrical interleaved rectangular grid 1201 as Figure 12a. As a result of setting the structures (S1, S2) to be the same and setting the offset vector to _1/2 ( _p Instead of interleaving two lattices, the same overall structure can be derived from a new lattice (L3) where the structure (S1) is repeated at each point of the lattice. Lattice L3 is represented by dots 1205 and dashed lines shown in FIG. 12B, neither of which are intended to convey physical structure.

Lattice vectors in Lattice (L3) and can be deduced by considering the geometry derived from the diagonal rows drawn through the lattice points. Figure 12c shows the lattice vector used to construct the lattice (L3) It shows two adjacent rows (1207, 1208) of a grid with . From this geometry, the angle α made by the rows of the grid with respect to the x-axis is given by (95),

(95)

Therefore, the angle ϕ ₂ subtended to the x-axis by the lattice vector h ₂ and the associated sine and cosine are given by (96), (97), (98).

(96)

(97)

(98)

The distance q ₂ between adjacent rows of a grid with grid vector h ₂ can be found from the geometry and is given by (99).

(99)

In row vector form, the grid vector h ₂ has a form similar to equation (26) and is given by (100)

(100)

This can be expressed as (101) in terms of p _x , p _y .

(101)

12D shows the lattice vector used to construct the lattice (L3) Shows adjacent rows (1209, 1210) of the grid with . The angle ϕ ₃ subtended to the x-axis by the grid vector h ₃ and its associated sine and cosine are given by (102), (103), (104).

(102)

(103)

(104)

The distance q ₂ between adjacent rows of a grid with grid vector h ₂ can be found from the geometry and is given by (105).

(105)

this is Same as In row vector form, the grid vector h ₂ has a form similar to equation (27) and is given by (106)

(106)

This can be expressed as (107) in terms of p _x , p _y .

(107)

We can use the expressions given in equations ( ₂₉ ) and (30) to determine the coordinates of the points of the lattice ( _L3 ) based on the parameterization of the lattice vectors h ₂ and h ₃ in terms of the lattice periods p . By replacing the parameters with expressions in the form of (29) and (30), (108) and (109) can be obtained,

(108)

and

(109)

here is the xy-coordinate of a point in the lattice (L3) indexed by the values a and b, which are positive or negative integers, or 0.

Since a and b in equations (108) and (109) are integers or 0, the quantities a+b and a-b must also be integers or 0. Also, if a+b is an even number, the evenness of a+b means that both a and b are odd or both are even, so a-b must also be even. Likewise, if a+b is odd, then a-b must also be odd.

If we assume that a+b is an even number, we can write (110) and (111),

(110)

and

(111)

Here, c,d are positive integers, negative integers, or 0. Therefore, the coordinates of points on the lattice for even values of a+b are given as (112),

(112)

Note that if i=c and j=d, this is equal to the coordinates of the lattice L1 given by equation (93). If instead we assume that a+b is odd, we can write (113) and (114),

(113)

and

(114)

Here, c,d are positive integers, negative integers, or 0. Therefore, the coordinates of points on the lattice for odd values of a+b are given as (115),

(115)

Note that if i=e and j=f, this is the same as the coordinates of the lattice L2 given by equation (94). Equations (112) and (115) prove that the points of the lattice (L3) are equal to the combination of the points of the lattice (L1) and lattice (L2), as given by equations (93) and (94), Therefore, it demonstrates the equivalence of the two approaches described for the construction of FSIRG. It has been shown that by constructing the FSIRG in terms of the lattice (L3), profound results can be deduced about the diffraction orders of the FSIRG.

Suppression of specific diffraction orders for FSIRG

Considering an FSIRG 1201 composed of a lattice L3, in terms of the grating vectors h ₂ , h ₃ given by equations (101) and (107), the grid equation (116) for the scattering of light beams from the lattice You can write .

(116)

Here, k _xy is the xy-wave vector of the beam incident on the grating, is the xy-wave vector is the diffraction order of the scattered beam with . Depending on the scattering properties of the wave from the diffraction grating, the order numbers l ₂ and l ₃ should be positive or negative integers, or 0. As previously mentioned, scattering from the lattice is also expected to satisfy the lattice equation (117).

(117)

Here, g ₂ and g ₃ are the lattice vectors given by equations (87) and (88), is the xy-wave vector is the diffraction order of the scattered beam with .

Note that equations (116) and (117) describe scattering from the same lattice. Therefore, the possible wavevectors of equation (116) and the possible wavevectors of equation (117) There must be an equivalent correspondence between the two. From this, the diffraction orders {l ₂ ,l ₃ } associated with the grating vectors h ₂ and h ₃ and the diffraction orders associated with the grating vectors g _x and g _y You should be able to draw some relationships between them. (118) and (1109) can be determined from the definitions of g _x , g _y , h ₂ and h ₃ given in equations (87), (88), (101) and (107), respectively,

(118)

and

(119)

Subtracting these results by equation (116) gives (120).

(120)

If this If set the same as the equation for, go Given (121) and (122), which must be true if describing the same vector as .

(121)

and

(122)

and By summing, (123) is given.

(123)

Since l ₂ is positive or negative, or 0, equation (123) shows that the diffraction order values m _x and m _y must be even or 0. However, based on the grid equation (117) for a rectangular grid, one can choose pairs of m _x and m _y values whose sum is odd. Since these pairs of values cannot correspond to the diffraction orders in equation (116), they create an apparent contradiction. The solution to this apparent contradiction is the _diffraction order where _m The diffraction efficiency of must be 0. Basically, the lattice equation (117) for a rectangular lattice shows that these orders exist in a mathematical sense, but the fact that their intensity is necessarily zero means that they do not exist physically, and therefore in terms of a physically measurable result. There is no contradiction. In this situation, both descriptions of FSIRG produce consistent predictions about the direction of the diffracted beam in the physical world. Since they arise from considering the lattices of the FSIRG and not the actual structures, these conclusions apply to all FSIRGs capable of scattering diffraction orders of granular light.

This result on the scattering properties of FSIRG can be confirmed by methods readily available to those skilled in the art. For example, by application of the Floquet-Bloch theorem using the symmetry of the lattice (L3) imposed on the solution for a plane wave scattered by an interleaved rectangular lattice, as defined here. Analytical calculations are possible. Alternatively, computational methods such as the finite-difference-time domain method (FDTD) with periodic boundary conditions, or rigorous coupled-wave analysis (RCWA) Semi-analytical methods such as wave analysis can be used.

Therefore, if a perfectly symmetric interleaved rectangular grating is properly configured for use as the output grating element of a DWC, such that the order nomenclature in Table 2 of Figure 70 is appropriate, all two-eye orders listed in Table 2 will result in a diffraction efficiency of zero. It can be stated that not only must it be of zero order, but only the conversion orders must be able to have non-zero efficiency. In other words, an output grating comprised of FSIRG cannot actually couple light out of the waveguide through the two-eye orders in Table 2.

Symmetry breaking to modify diffraction orders

FIG. 12E shows a cross-section of a pillar-shaped structure 1211 with a circular cross-section, and FIG. 12F shows a cross-section of a pillar-shaped structure 1212 with a square cross-section. Figure 12g shows an interleaved rectangular grid 1213 with the same period as FSIRG 1201. In IRG 1213, structure S1 is a circular cross-section pillar 1211 and structure S2 is a square cross-section pillar 1212. Because of the differences between the structures (S1, S2), it is better to construct the lattice using a single structure repeated at the points of a single lattice constructed from the vectors h ₂ and h ₃ given in equations (101) and (107). It is impossible anymore. Therefore, if If is odd, then the diffraction orders of the rectangular grating used to construct this IRG It can no longer be concluded that this necessarily has zero efficiency. Instead, the diffraction efficiency should depend on the shape of S1 and S2 and the difference in shape of the structures S1 and S2.

As will be proven, The diffraction efficiency of these odd orders is, It is particularly sensitive to the differences between the shapes of the structures (S1, S2) compared to the diffraction efficiency for orders where a is zero or even.

It is important to note that for this conclusion to apply, structures S1 or S2 need not consist of a single element. By way of example, Figure 12J shows structure S1 consisting of three circular pillars 1214 as shown in Figure 12H, and structure S2 consisting of two rectangular pillars 1215 as shown in Figure 12I. It shows an interleaved rectangular grid 1216 composed of . For this IRG, non-evanescent two-eye orders are expected to have non-zero diffraction efficiencies. When the IRG is formed by the structures S1 and S2 composed of three circular pillars 1214, the formed grid becomes an FSIRG whose two-eye order efficiency is necessarily 0.

The IRG unit cell described here is rectangular with sides aligned in the x- and y-directions, with a length in the x-direction equal to the x-period of the lattice (L1) (or equal to the lattice (L2)) The length in the y-direction is equal to the y-period of the lattice (L1) (or equal to the lattice (L2)). As above, the position of the unit cell relative to the periodic structure within the plane of the lattice can be chosen arbitrarily. IRG 1213 shown in Figure 12g shows several possible unit cells, indicated by dashed lines: one unit cell 1217 has structure S2 at its center, and the other possible simple unit cell 1218 has structure S2 at its center. With structure S1, another simple unit cell 1219 is configured to horizontally bisect two vertically adjacent copies of structure S1 and to vertically bisect two horizontally adjacent copies of structure S2. .

Symmetry breaking by compositional change

Another approach to introduce differences between structures S1 and S2 is to vary the composition of the structures in such a way that their optical properties are different. For example, if the structures are made to have different electrical permittivities, they will scatter light differently, resulting in an IRG that is no longer completely symmetrical and therefore Non-evanescent orders, where a is odd, do not necessarily have a diffraction efficiency of zero.

Symmetry breaking by changing lattice offset

Now the lattice offset vector between lattices L1 and L2 is no longer To avoid this, we consider a modification of FSIRG, where p _x and p _y are the periods of L1 and L2 in the x- and y-directions, respectively. With this change, it is no longer possible to construct a lattice using a single structure that repeats at the points of the lattice consisting of the vectors h ₂ and h ₃ shown in equations (101) and (107). thus, The argument leading to the requirement that diffraction orders where a is odd must have a diffraction efficiency of zero no longer applies.

Considering the very slight _{deviation of} the lattice offset vector from One might expect it to vary depending on the degree of the lattice offset vector derived from 1/2 (p _x , p _y ). thus, The diffraction efficiency of odd orders is, When compared to diffraction orders where is even or zero, It can be expected to exhibit much greater sensitivity to small deviations of the lattice offset vector from .

Method for efficiency control of diffraction orders

of the diffraction efficiency for specific diffraction orders by enabling both control of the position offset between the rectangular lattices L1 and L2 used to construct the interleaved rectangular lattice, as well as control of the difference between the structures S1 and S2. Additional control methods may be provided. In this way, perfectly symmetrical interleaved rectangular gratings and rectangular gratings have, on the one hand, certain diffraction orders necessarily being zero, and on the other hand, for similar structures the magnitudes of these orders have to be zero unless they are evanescent. These can be viewed as two extreme cases of a typical interleaved rectangular grid, providing cases that would typically be much larger.

For convenience, the following terminology is used to indicate the degree to which an IRG can deviate from an FSIRG: the degree to which the conformations of structures S1 and S2 differ from each other is referred to as the degree of broken conformational symmetry of the IRG; The degree to which the composition of S1 and S2 differs is referred to as the degree of disruption of the IRG; The overall degree of difference between structures S1 and S2, regardless of shape, composition, optical properties, or a combination thereof, is referred to as the degree of broken structural symmetry for the IRG; The position offset deviation between lattices L1 and L2 from is referred to as the degree of broken position symmetry of the IRG; Differences between structures S1 and S2 and/or The range in which the offset of lattices L1 and L2 deviates from is referred to as the degree of symmetry breaking of the IRG.

Referring to the criteria listed in Table 3 of Figure 71, obtaining a good level of performance from a rectangular grating when used as the output grating in a diffractive waveguide coupler requires a certain degree of control over the relative diffraction efficiency of the various conversion orders and two-eye orders. was found to be necessary. As will be demonstrated in the examples of the invention, the provision of additional control over the diffraction efficiency of two-eye diffraction orders made possible by the use of interleaved rectangular gratings with some controlled degree of symmetry breaking is achieved by the use of a diffractive waveguide coupler. It can provide advantageous performance in applications that use grids such as output devices.

Alternative arrangements for interleaved rectangular grids with high degree of symmetry

Figure 13A shows a top view of an example of a specific case of an interleaved rectangular grid 1301, referred to as a horizontally symmetric interleaved rectangular grid (HSIRG) and defined as an IRG with the specific properties below.

i) the period of the lattice L1 and L2 is p _x in the x-direction and p _y in the y-direction;

ii) The lattice offset vector is is given as;

iii) Structures S1 and S2 are identical and are assumed to be pillars with circular cross-section in the diagram shown here.

The diffraction orders for this grating follow equation (117). However, this lattice has an x-direction period of Note that it can be configured as a rectangular grid. As in the case of FSIRG, to reconcile the two methods for constructing HSIRG, it is required that the specific diffraction orders in equation (117) have a diffraction efficiency of zero. For HSIRG, if m _x is odd the orders will have zero efficiency. Referring to the diffraction orders listed in Table 2 of Figure 70, the only two-eye orders with non-zero efficiency are STE and TEAT-Y, and the conversion orders with non-zero efficiency are the backturn orders BT-X. , which means BT+X, BT-Y and BRT+Y. Other transition orders and two-eye orders are completely suppressed by this arrangement.

FIG. 13B shows a top view of an example of an interleaved grid 1302, referred to as a vertically symmetric interleaved rectangular grid (VSIRG) and defined as an IRG with the following specific properties:

i) the period of the lattice L1 and L2 is p _x in the x-direction and p _y in the y-direction;

ii) The lattice offset vector is is given as;

iii) Structures S1 and S2 are identical and are assumed to be pillars with circular cross-section in the diagram shown here.

The diffraction orders for this grating follow equation (117). However, this grid has a y-direction period of Note that it can be configured as a rectangular grid. As in the case of FSIRG, to reconcile the two methods for constructing VSIRG, it is required that the specific diffraction orders in equation (117) have a diffraction efficiency of zero. For VSIRG, if m _y is odd, the orders will have zero efficiency. Referring to the diffraction orders listed in Table 2 of Figure 70, the only two-eye orders with non-zero efficiency are TEAT+X and TEAT-X, and the conversion orders with non-zero efficiency are the inverse conversion orders BT-X, This means BT+X, BT-Y and BRT+Y. Other transition orders and two-eye orders are completely suppressed by this arrangement.

Similar to FSIRG, introduction of a degree of symmetry breaking due to departure from the exact conditions of HSIRG or VSIRG will result in non-evanescent diffraction orders that receive a portion of the energy from the incident light beam with zero efficiency. For small deviations, for a given direction, wavelength and polarization, the magnitude of the diffraction efficiency for the suppressed diffraction orders can be expected to depend on the optical properties, size and shape of the structures S1 and S2 as well as the extent of symmetry breaking. there is. With respect to HSIRG, the extent of the broken position symmetry is such that the lattice offset vector is It will be out of range. Similarly, with respect to HSIRG, the degree of broken position symmetry is It will be out of range.

Therefore, by taking the use of symmetry breaking, along with the concepts of FSIRG, HSIRG and VSIRG, the present invention provides a variety of approaches to provide significant control over a specific combination of two-arch orders or two-eye orders and transition orders. provides.

Advantages of using interleaved rectangular gratings as diffractive waveguide couplers in display systems

WO2018/178626 describes an approach for two-dimensional lattice design based on modified diamond structures. This approach has been shown to have certain scattering properties that are advantageous for use as an output grating for DWC. However, it has been found that in order to control the relative intensity of specific two-eye diffraction orders, it must be ensured that the parameters describing the morphology of the modified diamond are within certain ranges. This limits the extent to which the scattering properties of the grating can be optimized for improved performance, resulting in loss of control over the efficiency of certain two-eye diffraction orders, for example, by varying the shape of the diamond with respect to its position across the grating. This is because it leads to a loss of uniformity for the wearer. The interleaved rectangular grating described in the present invention can provide additional control over the scattering of the grating by using the degree of symmetry breaking in addition to the shape and optical properties of the grating structures. As a result, this can provide more control over the optimization of scattering characteristics to suit applications such as using IRG as the output element of a dwc.

An additional advantage of the present invention is that the diffraction orders that return the light beam in the input direction to the IRG are more easily accessible. Referring to Table 1 in FIG. 69, this represents light beams with cumulative orders of {0, -2}. The grating provided by the invention can provide more efficient coupling to this cumulative order than an approach such as that described in WO 2018/1786262 due to the reduction in the number of waveguide diffraction orders. This may allow a design that provides an increase in diffraction efficiency for diffraction orders leading to a cumulative order of {0, -2} without inducing excessive losses by scattering of beams for unwanted diffraction orders. The symmetry of the structure of many of the designs made possible by the present invention may also provide a more advantageous coupling to the cumulative order of {0, -2}. The possible paths for coupling the beam to order {0, -2} are diffraction of cumulative order {0, 0} by the BT-Y diffraction order, and { by the TTB+X, TTB-X diffraction orders. ±1, -1} Includes diffraction of cumulative order. Increasing the availability of directions such as {0, -2} cumulative order can improve the uniformity of the output from the DWC by providing more paths for the light beams through the waveguide, and thus the output resulting from the combination of these beams. Homogeneity can be further improved. Because these beam paths may provide more opportunities for light to be coupled out of the waveguide toward the observer, the use of light that is turned back may provide an increase in the overall efficiency of the DWC.

Another advantage of the present invention is that compared to the prior art, the size of the output grid can be smaller for a given size of the eyebox. This can be confirmed using pupil replication maps. The pupil replication map is a graph showing the location of positions where the output of the beam may occur as a result of the various branching paths through the DWC provided by repeated interactions with a diffractive element such as an IRG or other two-dimensional diffraction grating. . Basically, a copy of the input beam is assumed to be output at each output location. The result of the entire ensemble of beams is the dilated exit pupil described previously, which leads to the provision of an elongated eyebox. Therefore, the extent and coverage of the pupil replication map is one of the key factors that determine the eyebox of the system. It should be noted that for a given DWC, each input beam direction and wavelength will result in its own corresponding pupil replica map.

The projected eyebox for a given gaze angle is identified by taking the system's eyebox, which is at its defined position with respect to the DWC and usually spatially separated from the DWC, and projecting it back onto the DWC's output grid along the gaze angle. . The area of the output grid covered by this projected eyebox is the portion of the output grid that should output light at a given viewing angle to cover the eyebox at that viewing angle. For the image to be visible at all positions within the DWC's eyebox, pupil duplication events for a point in the viewing field of view must cover the corresponding projected eyebox at that point in the viewing field of view. Since light can be output from the DWC only at points where the diffraction grating is located, the extreme positions of the projected eyebox calculated over the entire viewing field projected by the DWC will set the minimum size of the output grating.

Figure 14a shows the pupil replication map 1401 of the DWC constructed according to the 2D diffraction grating described in WO 2018/178626. Here, only the dominant transition orders of the grid design are included when considering the allowed paths. The pupil replica map 1401 shows the position of the DWC's input grating 1402, which is a 1D diffraction grating with the grating vector pointing parallel to the y-axis of the graph. The output grating 1403 is a 2D diffraction grating according to WO 2018/178626 with grating vectors ±60° on the y-axis of the graph. Each pupil duplication event is indicated by a circle 1404. Here the pupil replication map for the top-right corner field is shown. The projected eyebox 1405 for this field is computed by projecting the observer's eye back onto the surface of the waveguide at the intended location.

For this grid, the pupil replication map shows that the xy-wavevector after one of the dominant transition orders points substantially in the diagonal direction. To ensure that the projected eyebox 1405 is covered by pupil replication events, the pupil should start transitioning at a significantly closer distance to the input grating than the eyebox 1405. This requires that the output grid have additional area above the most extreme eyebox location 1405, which increases the minimum size of the grid. In the example shown in Figure 14a, to achieve an eyebox of 11x12 mm with a viewing field of view of 35°Х20°, the output grid must have a minimum size of 38x30 mm.

Figure 14b shows a pupil replication map 1406 for a DWC with an output grid according to the present invention. Input grating 1407 is the same as input grating 1402, but output grating 1408 is an IRG with x- and y-periods equal to the period of input grating 1402. The viewing field of view of the projected display used with the display is the same. Compared to grating 1403, the pupil replica positions move further in the horizontal direction after the transition order from grating 1408. As a result, to ensure coverage for pupil duplication events, the additional space required above the projected eyebox 1409 can be much smaller, and the size of the output grid can be significantly reduced. In the example shown in Figure 14b, to achieve an 11x12 mm eyebox with a 35°x20° field of view, the output grid must have a minimum size of 27x30 mm. This is a reduction of 11 mm in the y-direction for the example in Figure 14a. Smaller grids reduce constraints on the size and shape of the overall DWC, potentially reducing manufacturing costs, as well as providing increased freedom over the form factor of designs incorporating DWCs using such grids.

Interleaved rectangular grid simulation methods of diffractive waveguide coupler

Although symmetry-based arguments can be used to determine that the efficiency of certain diffraction orders in a FSIRG, HSIRG, or VSIRG should be zero, it is often necessary to use a computer to determine the diffraction efficiency or associated polarization-dependent coefficient in an arbitrary IRG. It is important to emphasize the need to use computational techniques. As previously mentioned, appropriate methods include numerical techniques such as finite-difference-time domain method (FDTD) with periodic boundary conditions, or semi-analytical methods such as rigorous coupled wave analysis (RCWA).

In general, numerical simulation methods are needed to calculate the performance of IRGs in practical applications, such as those used as lattice elements in DWC. For situations where the coherence length of the light source used is shorter than the distance between successive grating interactions, a reasonable approximation is to consider each interaction independently of the other and use numerical ray-tracing to The purpose is to calculate the various beam paths resulting from successive interactions with the surface. The contribution of each of these paths to the overall output can be calculated taking into account the grid interactions required for a given path. The diffraction efficiency of various orders for each interaction can be calculated using the methods previously described for a given wavelength, direction and polarization of the incident beam, expressed as one or more rays. The subsequent radiation flux, direction and polarization of the various diffracted beams are then determined by the calculated diffraction efficiency as well as the grating equations acting on the xy-wavevectors described by the rays. By aggregating contributions from multiple paths and determining which contributions will be detected by the observer's representation, the output of a DWC can be simulated.

Ray-tracing methods have been widely applied to optical simulations, including systems featuring conduits and/or diffraction gratings. This method can be easily implemented through custom simulation codes or commercial software such as Zemax OpticStudio® (Zemax LLC). In ray-tracing simulations, a variety of real-world features can be considered for realizing the physical world of DWC. For example, the finite extent of a grid uses the hit coordinates of ray interactions with a surface, and tests whether those coordinates are within an area defined as having the grid can be described as a polygon or some other way. It can be considered by performing . The edges of the DWC itself can be defined by, for example, describing the edges using polygons, surfaces, or other primitive geometry, and performing tests to determine which surface a given ray will hit next on its path through the DWC. It can be simulated using ray-tracing. Processes such as absorption or scattering can then be applied to the ray based on the surfaces it strikes. In this way, sophisticated simulation models of the behavior of DWCs can be developed and used to predict their performance.

Design and representation methods of interleaved rectangular grids

For light to be scattered in a diffraction grating, there must be a change in at least one optical property in and around the grating, including but not limited to refractive index, electrical permittivity, permeability, birefringence, and/or absorptivity. In many cases, these changes are achieved using embedded structures of at least one different optical property within a matrix of surrounding materials, or as surface relief structures consisting of at least one material on a substrate of the same or a different material. can be, which protrudes into the surface relief structure and other surrounding media. In order to diffract light, at least one optical property of the medium surrounding the surface relief structure must differ from at least a portion of the surface relief structure. The ground medium commonly used for gratings disposed as surface relief structures on the surface of a DWC is air, but this need not be the case. In a sense, surface relief structures can be considered structures embedded in the matrix of the surrounding medium. Similar methods can be used to design and represent surface relief structures and embedded structures.

The design of the lattice will require a representation or description that provides details about the shape and composition of the IRG so that it can be designed, simulated, and manufactured in the physical field. Here, various expressions suitable for describing various surface relief structures are developed to explain various aspects of the invention as well as to demonstrate how such aspects can be realized in practical applications such as simulation and manufacturing. It will be appreciated by those skilled in the art that there is a wide range of methods that can be used for executable expression of IRGs beyond those described herein.

Design and representation method of interleaved rectangular grid geometry based on mathematical structure

In some approaches, lattices can be created from three-dimensional structures created from one or more materials. For grids constructed according to these principles, mathematical equations can describe the geometry at each interface between the various materials used. In some approaches, representation may involve augmentation of the geometries, such as the addition of layers of new geometries derived from existing geometries, to represent the results of processes such as coating. In another approach, one may consider modifications to the geometry of the lattice, such as rounding of sharp features, as a tool to change the performance of the design or as a way to reveal manufacturing limitations. One can consider applying these approaches in various combinations and multiple times, potentially yielding quite complex geometries consisting of many distinct regions of different materials.

In a system where materials are described by surface geometry, each material must be associated with a description of its own surface geometry. One method for generating a description of the surface geometry of an interleaved rectangular grid includes the following steps.

The diffraction orders for this grating follow equation (117). However, this lattice has an x-direction period of Note that it can be configured as a rectangular grid. As in the case of FSIRG, to reconcile the two methods for constructing HSIRG, it is required that the specific diffraction orders in equation (117) have a diffraction efficiency of zero. For HSIRG, if m _x is odd the orders will have zero efficiency. Referring to the diffraction orders listed in Table 2 of Figure 70, the only two-eye orders with non-zero efficiency are STE and TEAT-Y, and the conversion orders with non-zero efficiency are the backturn orders BT-X. , which means BT+X, BT-Y and BRT+Y. Other transition orders and two-eye orders are completely suppressed by this arrangement.

FIG. 13B shows a top view of an example of an interleaved grid 1302, referred to as a vertically symmetric interleaved rectangular grid (VSIRG) and defined as an IRG with the following specific properties:

i) the period of the lattice L1 and L2 is p _x in the x-direction and p _y in the y-direction;

ii) The lattice offset vector is is given as;

iii) Structures S1 and S2 are identical and are assumed to be pillars with circular cross-section in the diagram shown here.

The diffraction orders for this grating follow equation (117). However, this grid has a y-direction period of Note that it can be configured as a rectangular grid. As in the case of FSIRG, to reconcile the two methods for constructing VSIRG, it is required that the specific diffraction orders in equation (117) have a diffraction efficiency of zero. For VSIRG, if m _y is odd, the orders will have zero efficiency. Referring to the diffraction orders listed in Table 2 of Figure 70, the only two-eye orders with non-zero efficiency are TEAT+X and TEAT-X, and the conversion orders with non-zero efficiency are the inverse conversion orders BT-X, This means BT+X, BT-Y and BRT+Y. Other transition orders and two-eye orders are completely suppressed by this arrangement.

Similar to FSIRG, introduction of a degree of symmetry breaking due to departure from the exact conditions of HSIRG or VSIRG will result in non-evanescent diffraction orders that receive a portion of the energy from the incident light beam with zero efficiency. For small deviations, for a given direction, wavelength and polarization, the magnitude of the diffraction efficiency for the suppressed diffraction orders can be expected to depend on the optical properties, size and shape of the structures S1 and S2 as well as the extent of symmetry breaking. there is. With respect to HSIRG, the extent of the broken position symmetry is such that the lattice offset vector is It will be out of range. Similarly, with respect to HSIRG, the degree of broken position symmetry is It will be out of range.

Therefore, by taking the use of symmetry breaking, along with the concepts of FSIRG, HSIRG and VSIRG, the present invention provides a variety of approaches to provide significant control over a specific combination of two-arch orders or two-eye orders and transition orders. provides.

Advantages of using interleaved rectangular gratings as diffractive waveguide couplers in display systems

WO2018/178626 describes an approach for two-dimensional lattice design based on modified diamond structures. This approach has been shown to have certain scattering properties that are advantageous for use as the output grating of a DWC. However, it has been found that in order to control the relative intensity of specific two-eye diffraction orders, it must be ensured that the parameters describing the morphology of the modified diamond are within certain ranges. This limits the extent to which the scattering properties of the grating can be optimized for improved performance, resulting in loss of control over the efficiency of certain two-eye diffraction orders, for example, by varying the shape of the diamond with respect to its position across the grating. This is because it leads to a loss of uniformity for the wearer. The interleaved rectangular grating described in the present invention can provide additional control over the scattering of the grating by using the degree of symmetry breaking in addition to the shape and optical properties of the grating structures. As a result, this can provide more control over the optimization of scattering characteristics to suit applications such as using IRG as the output element of a dwc.

An additional advantage of the present invention is that the diffraction orders that return the light beam in the input direction to the IRG are more easily accessible. Referring to Table 1 in FIG. 69, this represents light beams with cumulative orders of {0, -2}. The grating provided by the invention can provide more efficient coupling to this cumulative order than an approach such as that described in WO 2018/1786262 due to the reduction in the number of waveguide diffraction orders. This may allow a design that provides an increase in diffraction efficiency for diffraction orders leading to a cumulative order of {0, -2} without inducing excessive losses by scattering of beams for unwanted diffraction orders. The symmetry of the structure of many of the designs made possible by the present invention may also provide a more advantageous coupling to the cumulative order of {0, -2}. The possible paths for coupling the beam to order {0, -2} are diffraction of cumulative order {0, 0} by the BT-Y diffraction order, and { by the TTB+X, TTB-X diffraction orders. ±1, -1} Includes diffraction of cumulative order. Increasing the availability of directions such as {0, -2} cumulative order can improve the uniformity of the output from the DWC by providing more paths for the light beams through the waveguide, and thus the output resulting from the combination of these beams. Homogeneity can be further improved. Because these beam paths may provide more opportunities for light to be coupled out of the waveguide toward the observer, the use of light that is turned back may provide an increase in the overall efficiency of the DWC.

Another advantage of the present invention is that compared to the prior art, the size of the output grid can be smaller for a given size of the eyebox. This can be confirmed using pupil replication maps. The pupil replication map is a graph showing the location of positions where the output of the beam may occur as a result of the various branching paths through the DWC provided by repeated interactions with a diffractive element such as an IRG or other two-dimensional diffraction grating. . Basically, a copy of the input beam is assumed to be output at each output location. The result of the entire ensemble of beams is the dilated exit pupil described previously, which leads to the provision of an elongated eyebox. Therefore, the extent and coverage of the pupil replication map is one of the key factors that determine the eyebox of the system. It should be noted that for a given DWC, each input beam direction and wavelength will result in its own corresponding pupil replica map.

The projected eyebox for a given gaze angle is identified by taking the system's eyebox, which is at its defined position with respect to the DWC and usually spatially separated from the DWC, and projecting it back onto the DWC's output grid along the gaze angle. . The area of the output grid covered by this projected eyebox is the portion of the output grid that should output light at a given viewing angle to cover the eyebox at that viewing angle. For the image to be visible at all positions within the DWC's eyebox, pupil duplication events for a point in the viewing field of view must cover the corresponding projected eyebox at that point in the viewing field of view. Since light can be output from the DWC only at points where the diffraction grating is located, the extreme positions of the projected eyebox calculated over the entire viewing field projected by the DWC will set the minimum size of the output grating.

Figure 14a shows the pupil replication map 1401 of the DWC constructed according to the 2D diffraction grating described in WO 2018/178626. Here, only the dominant transition orders of the grid design are included when considering the allowed paths. The pupil replica map 1401 shows the position of the DWC's input grating 1402, which is a 1D diffraction grating with the grating vector pointing parallel to the y-axis of the graph. The output grating 1403 is a 2D diffraction grating according to WO 2018/178626 with grating vectors ±60° on the y-axis of the graph. Each pupil duplication event is indicated by a circle 1404. Here the pupil replication map for the top-right corner field is shown. The projected eyebox 1405 for this field is computed by projecting the observer's eye back onto the surface of the waveguide at the intended location.

For this grid, the pupil replication map shows that the xy-wavevector after one of the dominant transition orders points substantially in the diagonal direction. To ensure that the projected eyebox 1405 is covered by pupil replication events, the pupil should start transitioning at a significantly closer distance to the input grating than the eyebox 1405. This requires that the output grid have additional area above the most extreme eyebox location 1405, which increases the minimum size of the grid. In the example shown in Figure 14a, to achieve an eyebox of 11x12 mm with a viewing field of view of 35°Х20°, the output grid must have a minimum size of 38x30 mm.

Figure 14b shows a pupil replication map 1406 for a DWC with an output grid according to the present invention. Input grating 1407 is the same as input grating 1402, but output grating 1408 is an IRG with x- and y-periods equal to the period of input grating 1402. The viewing field of view of the projected display used with the display is the same. Compared to grating 1403, the pupil replica positions move further in the horizontal direction after the transition order from grating 1408. As a result, to ensure coverage for pupil duplication events, the additional space required above the projected eyebox 1409 can be much smaller, and the size of the output grid can be significantly reduced. In the example shown in Figure 14b, to achieve an 11x12 mm eyebox with a 35°x20° field of view, the output grid must have a minimum size of 27x30 mm. This is a reduction of 11 mm in the y-direction for the example in Figure 14a. Smaller grids reduce constraints on the size and shape of the overall DWC, potentially reducing manufacturing costs, as well as providing increased freedom over the form factor of designs incorporating DWCs using such grids.

Interleaved rectangular grid simulation methods of diffractive waveguide coupler

Although symmetry-based arguments can be used to determine that the efficiency of certain diffraction orders in a FSIRG, HSIRG, or VSIRG should be zero, it is often necessary to use a computer to determine the diffraction efficiency or associated polarization-dependent coefficient in an arbitrary IRG. It is important to emphasize the need to use computational techniques. As previously mentioned, appropriate methods include numerical techniques such as finite-difference-time domain method (FDTD) with periodic boundary conditions, or semi-analytical methods such as rigorous coupled wave analysis (RCWA).

In general, numerical simulation methods are needed to calculate the performance of IRGs in practical applications, such as those used as lattice elements in DWC. For situations where the coherence length of the light source used is shorter than the distance between successive grating interactions, a reasonable approximation is to consider each interaction independently of the other and use numerical ray-tracing to The purpose is to calculate the various beam paths resulting from successive interactions with the surface. The contribution of each of these paths to the overall output can be calculated taking into account the grid interactions required for a given path. The diffraction efficiency of various orders for each interaction can be calculated using the methods previously described for a given wavelength, direction and polarization of the incident beam, expressed as one or more rays. The subsequent radiation flux, direction and polarization of the various diffracted beams are then determined by the calculated diffraction efficiency as well as the grating equations acting on the xy-wavevectors described by the rays. By aggregating contributions from multiple paths and determining which contributions will be detected by the observer's representation, the output of a DWC can be simulated.

Ray-tracing methods have been widely applied to optical simulations, including systems featuring conduits and/or diffraction gratings. This method can be easily implemented through custom simulation codes or commercial software such as Zemax OpticStudio® (Zemax LLC). In ray-tracing simulations, a variety of real-world features can be considered for realizing the physical world of DWC. For example, the finite extent of a grid uses the hit coordinates of ray interactions with a surface, and tests whether those coordinates are within an area defined as having the grid can be described as a polygon or some other way. It can be considered by performing . The edges of the DWC itself can be defined by, for example, describing the edges using polygons, surfaces, or other primitive geometry, and performing tests to determine which surface a given ray will hit next on its path through the DWC. It can be simulated using ray-tracing. Processes such as absorption or scattering can then be applied to the ray based on the surfaces it strikes. In this way, sophisticated simulation models of the behavior of DWCs can be developed and used to predict their performance.

Design and representation methods of interleaved rectangular grids

For light to be scattered in a diffraction grating, there must be a change in at least one optical property in and around the grating, including but not limited to refractive index, electrical permittivity, permeability, birefringence, and/or absorptivity. In many cases, these changes are achieved using embedded structures of at least one different optical property within a matrix of surrounding materials, or as surface relief structures consisting of at least one material on a substrate of the same or a different material. can be, which protrudes into the surface relief structure and other surrounding media. In order to diffract light, at least one optical property of the medium surrounding the surface relief structure must differ from at least a portion of the surface relief structure. The ground medium commonly used for gratings disposed as surface relief structures on the surface of a DWC is air, but this need not be the case. In a sense, surface relief structures can be considered structures embedded in the matrix of the surrounding medium. Similar methods can be used to design and represent surface relief structures and embedded structures.

The design of the lattice will require a representation or description that provides details about the shape and composition of the IRG so that it can be designed, simulated, and manufactured in the physical field. Here, various expressions suitable for describing various surface relief structures are developed to explain various aspects of the invention as well as to demonstrate how such aspects can be realized in practical applications such as simulation and manufacturing. It will be appreciated by those skilled in the art that there is a wide range of methods that can be used for executable expression of IRGs beyond those described herein.

Design and representation of interleaved rectangular grid geometries based on mathematical structures

In some approaches, lattices can be created from three-dimensional structures created from one or more materials. For grids constructed according to these principles, mathematical equations can describe the geometry at each interface between the various materials used. In some approaches, representation may involve augmentation of the geometries, such as the addition of layers of new geometries derived from existing geometries, to represent the results of processes such as coating. In another approach, one may consider modifications to the geometry of the lattice, such as rounding of sharp features, as a tool to change the performance of the design or as a way to reveal manufacturing limitations. One can consider applying these approaches in various combinations and multiple times, potentially yielding quite complex geometries consisting of many distinct regions of different materials.

In a system where materials are described by surface geometry, each material must be associated with a description of its own surface geometry. One method for generating a description of the surface geometry of an interleaved rectangular grid includes the following steps.

One. Assume the bottom of the grid is the xy-plane (i.e. z=0). The lattice vectors used to construct the lattices (L1, L2) of the IRG are defined as (124) and (125).

(124)

and

(125)

2. To account for the finite range of the IRG, a cropping function C(x,y) is defined. C(x,y) has a value of 1 in the region where the grid exists, and 0 in all other regions. It has a value of Therefore, if cropping is not needed, C(x,y)=1 regardless of the (x,y)-coordinates.

3. Lattice L1 is expressed as the lattice function L_1 (x,y) given by (126),

(126)

Lattice L2 is the lattice function given by (127) It is expressed as

(127)

here, is the grid offset vector.

5. Surface geometry function is defined as the representation of the structure S1 of the IRG, which describes the distance in the z-direction over which the structure protrudes from the lattice plane as a function of the (x,y)-coordinates. Similarly, the function is defined as the representation of the structure S2 of the IRG. function and may be a mathematical function, the output of a computational algorithm, a grid or mesh of discrete values combined with an interpolation scheme, or a set of parametric surfaces, such as Non-Uniform Rational B-Spline surfaces. Importantly, here for definition the function and means that only a single value must be returned for each (x,y)-coordinate input. and are all defined to have non-zero values only within a rectangular region in the xy-plane of the same size and orientation as the unit cell of the IRG, which is a rectangle with length p _x in the x-direction and length p _y in the y-direction. Typically, this area is centered at the origin (0,0), but this does not have to be the case.

5. Based on the representation of lattice L1 and structure S1, structure function and lattice function A periodic surface geometric function defined as (128) which is the convolution of The periodic structure PS1 can be expressed by .

(128)

Here, the symbol a(x,y)*b(x,y) represents the two-dimensional convolution of functions a() and b() in (x,y) space. is a (x,y)-coordinate function that represents the distance in the z-direction over which the periodic structure protrudes from the plane of the lattice. Similarly, the periodic structure PS2 can be expressed by the periodic surface geometry function (129).

(129)

Performing the convolution of equations (128) and (129) gives (130) and (131).

(130)

and

(131)

These definitions ensure that the IRG always contains full copies of structures S1 and S2.

6. IRG is constructed by combining PS1 and PS2 together, and is expressed as the IRG surface function I(x,y). This describes the distance in the z-direction over which the coupled periodic structure protrudes from the plane of the lattice as a function of the (x,y)-coordinate. periodic structure function and The combination can be performed in various ways. The simplest approach is to add a structure that gives (132).

(132)

However, if the non-zero regions of both structure functions overlap, the structures are stacked on top of each other. This may not reflect design intent or conform to manufacturing limitations. A more general combination method can be defined using a masking function defined as (133).

(133)

Product of mask functions evaluated for each periodic structure given (x,y)-coordinates By calculating , it is possible to mathematically identify the part of the lattice where the two structures overlap. To determine the IRG surface function in overlapping regions, a combiner function X(a,b) can be defined, which can be composed of various equations depending on the intent and requirements of the equation. Valid definitions for combiner functions include, but are not limited to, the examples below:

Therefore, the IRG surface function can be defined as (143).

(143)

In some formulations, it may be helpful to have the periodic structure function have a range of values that make it difficult to use z=0 as a criterion for determining whether two structures exist and therefore whether an overlap occurs. Instead, masking functions are required to represent the intended structure. and It can be defined based on the detection of a special designated value ξ chosen to be easily distinguishable from the range of values of . In this case, the mask function can be defined as (144).

(144)

If the IRG surface function is defined to have a value of P ₀ in a region where the two periodic structure functions are not defined, the IRG function can be defined as (145).

(145)

This completes the description of the layers of the IRG's geometry. Multiple layers can be calculated according to the same procedure. These layers can be positioned relative to each other by applying a position shift to the surface functions of the IRG, where these shifts may be in the x-, y- and/or z-directions.

In the previous formula and are all defined to have a non-zero value only within a rectangular area of the same size as the IRG unit cell of the IRG. Typically, this area is centered at the origin (0,0), but this does not have to be the case. Outside this rectangular area, and is 0 by definition. This can be enforced using the rectangle function, rect(x), defined as (146).

(146)

if, If is a function that does not follow the rule of being zero outside the IRG unit cell, the appropriate truncated version of this function centered at the origin (0,0) is given by (147).

(147)

From equation (147) itself, and Limits the scope of defined structures. However, in some systems it may be desirable to exhibit a range of structures that extend beyond the limits of the IRG unit cell, as this may result in beneficial properties for the performance of the IRG. From the definition of periodic structures, we know that everything about the shape of the structure can be expressed within the IRG unit cell. Therefore, in order to display long structures, a method is needed to accommodate them within a single unit cell.

FIG. 15A shows a top view of a portion of IRG 1501 in which structures S1 and S2 are comprised of pillars 1502 and 1503, respectively, which have an extent in the y-direction that is longer than the y-dimension of the IRG unit cell. . A rectangular area 1504 of the same dimensions as the IRG unit cell may be drawn around one of the copies of structure S1, and similarly a rectangular area 1505 may be drawn around one of the copies of structure S2. . An appropriate structure function S ₁ (x,y), which is defined entirely within the unit cell rectangle 1504, can be defined by finding the portion of the periodic array of structures PS1 that lies within the rectangle 1504.

Figure 15b shows the periodic structure (PS1) of IRG 1501 lying within rectangle 1504. A copy 1506 of structure S1 lies in the center of the rectangle and extends beyond the top and bottom edges of the structure. To form the structure function S ₁ (x,y), first crop the structure S1 crossing the top edge 1507 and the bottom edge 1509. By adding some of the vertically adjacent copies of structure S1 overlapping with rectangles 1504 leading to additional features at the bottom 1508 and top 1510 of the structure function S ₁ (x,y), the unit cell is It is completed. A structure function S ₂ (x,y) within a rectangle 1505 and for structures extending beyond the x-direction limits of the unit cell length or structures extending beyond the x- and y-direction limits of the unit cell rectangle. Uniform procedures may be applied.

A mathematical expression of this process can be constructed by taking the sum of shifted versions of the structure function that describes the overall structure, but truncating each of them into a unit cell rectangle. Figure 15C shows a single structure S1 1513 placed in the center of unit cell rectangle 1504, with additional rectangles of the same size as 1504, 1511, and 1512 placed at the top and bottom of 1504, respectively, as shown. . The portion of S1 that should be wrapped by rectangle 1504 is visible within each of these rectangles. Mathematically, if If is a function that describes a structure that extends beyond the unit cell rectangle, then the structure function S ₁ (x,y), which is restricted exactly to a single unit cell, is given by (148).

(148)

here, is assumed to have a value of 0 outside the part required for the structure. If the value of ξ is used to indicate a lack of structure, a masking function leading to equation (149) can be used.

(149)

Equations (148) and (149) can be generalized to as many adjacent rectangles as necessary to ensure that the structure is accurately represented by the structure function confined within a single unit cell. For example, a unit cell rectangle is desired to be extended into eight surrounding rectangles (horizontal and vertical edges, diagonal corners), and if If is a function that describes an extended structure, the structure function wrapped in a rectangle of unit cell size is given by (150).

(150)

Here, the part without structure is Assuming that , if a replacement value is used to indicate the lack of structure, a mask function can be used as demonstrated by equation (149).

When structures S1 or S2 are repeated on the respective lattices, overlapping each other within their own periodic structures, the procedure described here results in the structures having the sum of the heights of the overlapping components. This does not preclude the use of this procedure, but should be kept in mind when designing structures and considering the suitability of cyclic structures once repeated.

In addition to extending beyond the IRG unit cell, it is also possible for the periodic structures PS1 and PS1 to be composed of continuous structures. In this case, an appropriate structure function would be one defined entirely within a rectangle of the same dimensions as the IRG unit cell, with opposing edges aligned together to join to form a continuous structure. Figure 15D shows IRG 1514 consisting of structures 1515 and 1516, which are continuous in the y-direction with respect to both periodic structures PS1 and PS2, respectively. Figure 15e shows a suitable structure (S1) for creating a periodic structure (PS1) as defined within a rectangle of the same dimensions as the unit cell 1517. The edges 1518, 1519 of the structure allow a single continuous structure to be formed when unit cells are placed adjacent to each other. Note that, in essence, a continuous structure is simply an isolated structure of size and shape within a unit cell that, when repeated over a periodic array, is adjacent to its own copies to form a continuous structure. Accordingly, the definition of an interleaved rectangular grid can include isolated structures as well as continuous structures.

A common class of structures consists of one or more shaped profiles that protrude in the z-direction to form pillars. If the structure is formed from pillars that all protrude to the same height, the resulting structures are often referred to as binary structures. If the profile of the pillar can be described by a polar function of angle ρ(θ) in the xy-plane, the definition of the appropriate structure function S(x,y) is given by (151).

(151)

Here h is the height of the pillar and θ=atan2(y,x) is used. Here, atan2(y,x) is a quadrant-sensitive arc-tangent to find the value of the polar angle θ when converting from Cartesian (x,y)-coordinates to polar (ρ,θ)-coordinates. tangent) function. In another approach to describe the extruded surface geometry, we can define an N-sided polygon P as a list of (x,y)-coordinates for the N vertices of the polygon, , here, is a list of (x,y) coordinate pairs of polygon P. Afterwards, a function with the following characteristics can be defined.

(152)

Therefore, the structure function S(x,y) corresponding to a single structure will be (153).

(153)

The height of the ith structure is h _i , and the x- and y-coordinates of the polygon of the ith structure are Multiple structures given by can be expressed as the structure function (154).

(154)

Here, M is the number of elements in the structure. In this way, sophisticated multi-device structures can be created. It should be noted that this approach can also be applied to create multilevel structures. By defining polygons that lie on top of each other, equation (154) can be used to represent a multilevel structure.

After constructing a surface representation through mathematical formulas, it often needs to be converted to a format suitable for other purposes, such as simulation or fabrication. The format required will be determined by the requirements of the process, but there are many methods available to those skilled in the art, which can be applied in a simple manner.

For example, in some applications, the grid may need to be represented as a mesh of triangular polygons. The mathematical expression can be converted to mesh form by first constructing a triangular mesh in the xy-plane, then evaluating a mathematical function at each vertex of this mesh to obtain the z-value of the mesh. The result will be a mesh of triangular curves that approximates a mathematical function. These representations will necessarily be approximations of the actual geometry; For example, infinitely steep walls in a structure caused by sudden steps in z-values will be limited by the choice of mesh resolution around such transitions.

However, the resolution of the grid may be adjusted so that for practical purposes the difference between the approximate and actual representations is essentially negligible. Some uses may require a voxel-based representation of the grid. A voxel-based description is presented as a three-dimensional grid of coordinates where one or more values of interest are described at each coordinate.

These values will generally be properties of the material related to its interaction with electromagnetic radiation, such as electrical permittivity. A voxel representation can be constructed by first creating a three-dimensional grid of size and resolution dictated by the requirements. A grid is considered to describe the edge vertices of a set of continuous three-dimensional cuboids, the voxels of which are expressed. Each voxel is typically a Cartesian square about the center of the cuboid, calculated as the arithmetic mean of the coordinates with respect to the edge vertices. -Associates a set of properties {V_i} with coordinates, intrinsic optical properties and/or requirements for the representation, such as an index value that describes the material in the voxel. Here, the index i is used to indicate the ith voxel of the representation.

Afterwards, the transformation of the mathematical expression into voxel space is repeated over all voxels, according to the material assignment of the geometry of the surface, and for each voxel the z-value of the voxel center and the value of the function at each point are calculated. This can be achieved by comparing.

For example, assume that an IRG composed of a material with a refractive index n ₂ is placed on a substrate with a material with a refractive index n ₁ and is surrounded by a medium with a refractive index n ₀ . If the substrate surface is located at z=0 and the definition of the IRG function I(x,y) is If so, we know that the material of the system with z≤0 is the material of the substrate, and the material with z>I(x,y) is the surrounding material. Between these limitations, the material will become that of the IRG. Therefore, the coordinates In the ith voxel with , the refractive index n _i can be determined by equation (155) below.

(155)

This procedure provides a complete set of properties, through substitution of the refractive index value for the value of the relevant properties. It can be applied throughout. Alternatively, in some systems equation (155) can be used, but the refractive indices can be replaced by exponent values corresponding to the material choice. A separate look-up table of material property values can be associated with each material index value. As with the mesh representation, the voxel-based representation will generally be an approximation of the principle representation, but by adjusting the resolution of the voxel grid, the differences can be negligible from a practical standpoint.

Ultimately, the accuracy of numerical expressions will be determined by the limitations of computer resources such as memory and computing power. Fortunately, the computing power of modern personal computers has been found to be sufficient to handle a wide range of designs and representations with sufficient precision.

Design and expression method of interleaved rectangular grid geometry based on 3D geometric modeling technique

The procedure leading to the IRG surface function given in equation (143) requires that the resulting surface geometry have a single z-value in each (x,y)-coordinate. This precludes the description of certain geometries, such as those where the geometry is characterized by structures with more than one z-value in some (x,y)-coordinates, such as undercut geometries or highly sloped faces. Instead of finding a mathematical description of the structures S1 and S2, a method developed for the design of three-dimensional geometries, such as those used in three-dimensional computer aided design systems (CAD) or three-dimensional computer graphics systems You can create these structures using .

These systems generally include tools for extruding, lofting, and sweeping 2D profiles, 3D geometric primitives such as cubes, cylinders, ellipsoids, and tetrahedra, tools for creating and manipulating polygonal meshes, and tools for creating and manipulating polygonal meshes. It provides a variety of geometric modeling processes for tools that can create and manipulate curved surfaces, including non-uniform rational B-splines (NURBS)-based tools that can be used to express range geometries. Typical computer modeling systems also allow for geometric combinations through operations such as geometric combination (also called Boolean union, Boolean combination, and addition, in various modeling systems), geometric intersection, and geometric subtraction. It provides tools for joining structures, as well as a wide range of tools for trimming, stitching, blending, distortion and other manipulations. By sequentially applying these geometric modeling and generation tools and combining multiple elements, complex three-dimensional structures of a wide range of geometries can be created.

Commercially available software that demonstrates how to create and modify the geometries described herein includes SolidWorks® (Dassault Systemes SolidWorks Corporation), Catia (Dassault Systemes SE), and Autodesk Maya (Autodesk, Inc). Examples of open-source software include the Blender project and FreeCAD (both licensed under GPLv2+).

In general, the geometry modeled on a given system can be exported to several vendor-neutral file formats. Suitable formats that can describe various types of geometry include IGES (Initial Graphics Exchange Specification) and STEP (Standard for the Exchange of Product model data) file formats. For data converted to a polygonal mesh, there are the STL (stereolithography) file format from 3D Systems Corporation and the PLY (Polygon) file format developed at Stanford University. These files can then be imported for use in simulation and manufacturing software. The specifications for these file formats are publicly available, so if a given system does not support the required format, software modules can be written to import the data and use it to create a physical world implementation of the described geometry or design. It can be analyzed in a format suitable for future purposes, such as simulation of the scattering properties of grid designs based on the creation of manufacturing tools. This import routine can also perform labeling of the material types of the various entities described by the file and assign material properties and labels as needed.

Although these systems are intended to generate much larger structures, it is important to understand that it is simple to integrate scaling functionality into a simulation tool that uses the geometries generated by such systems. For example, 1 mm in a CAD system may be scaled to correspond to 1 nm in a simulation system. Additionally, it is important to understand that only a single unit cell of an IRG needs to be modeled in a CAD system and exported to simulation or other design tools. If necessary, replication of the structure into an entire array can be performed, but for some purposes, such as simulations of scattering of electromagnetic waves in periodic structures, typically only a single unit cell is required due to the invocation of periodic boundary conditions as part of the simulation process. need.

Figure 16A shows, for example, a cylindrical structure 1601, a spherical structure 1602, and a cubic structure 1603. After placing a sphere 1602 on the end of a cylinder 1601 and performing a geometric combination operation, placing the result on a cube 1603 and performing another geometric union operation creates a composite structure 1604. can be created. This structure can be used as structure S1 or S2 of IRG.

Structures S1 and S2 should be configured to be completely defined within a rectangular area of the xy-plane of the same dimensions and orientation as the IRG unit cell in the x- and y-directions respectively. This may require taking a portion of the structures that overlap the edge of the IRG unit cell to create a version of the structure within the IRG unit cell using copy and trip operations. For example, the elongated structure 1502 that forms part of the IRG 1501 shown in FIG. 15A can be replaced with the modified multi-element structure shown in FIG. 15B, which results in an overall single unit cell 1504. defined within. This modified structure is formed by taking three consecutive copies of structure 1501 from vertically adjacent unit cells and trimming the structures so that only the portions that lie in a single unit cell remain. The editing process of these geometries is simplified with modern three-dimensional modeling tools such as those mentioned previously.

In this method, periodic structures PS1 and PS2 are created in a simple pattern replication operation where a copy of structure S1 is placed at each point of the lattice (L1) of the IRG, and a copy of structure S2 is placed at each point of the lattice (L2) of the IRG. will be created by This is similar to the convolution operation shown in equations (128) and (129). A geometric union operation of adjacent copies of structures S1 and S2 can be used to join the structures together to form periodic structures PS1 and PS2, respectively.

IRG is formed by the combination of periodic structures PS1 and PS2. In this method, how to handle the overlap area of PS1 and PS2 must be considered when configuring the IRG. Typically this combination will be a geometric union of structures. If PS1 and PS2 are configured as closed geometries, tests can be performed to determine if the geometry in one region is within the other region, thereby determining the appropriate trip and stitch operations needed to create the geometry union. If open surfaces are used in PS1 and PS2, it is advisable to add additional geometry to the representation to create one of more closed bodies so that operations such as geometry union can be applied correctly in three dimensions. Generally advantageous. One method is to use extrusion operations in a plane parallel to the xy-plane. Figure 16b shows a portion of the unclosed surface 1605 showing a periodic structure of protrusions in the z-direction. The profile of surface 1605 parallel to the xy-plane can be used to define plane 1606. Extrusion in the z-direction from surface 1605 to surface 1606 creates a closed geometry 1607 suitable for geometric union operations.

In some embodiments, the IRG will be a surface relief structure on the substrate. This combination can be achieved by a geometric union between the IRG and a cube with faces parallel to the xy-plane of the IRG. If the substrate has different optical properties than the IRG, such as composed of a different material, the boundary between the substrate and the IRG should be maintained in a geometric representation, and the optical properties of the overlapping geometries between the substrate and the IRG should be or some combination of the two must be selected to determine whether the optical properties are the optical properties. For these IRGs to be physically realized, all parts of the surface relief structure must be bonded to the substrate in some way.

In other embodiments, the IRG will be embedded in a medium M such as the substrate itself, where the optical properties of the medium and the IRG differ in at least one respect. Figure 16c shows the surface relief structure 1608 to be embedded within the medium M. A geometrical representation of the medium M can be constructed by extruding a 2D profile in the xy-plane in the z direction. The resulting slab 1609 must have coverage in at least the x, y, and z-directions of the IRG. A representation combining the medium M and IRG can be achieved by first geometrically subtracting a copy of the surface relief structure 1608 from the slab 1609, resulting in a slab 1610 with the IRG geometry truncated. The geometric union of this cut slab 1610 and the surface relief structure 1608 with the internal surfaces between the IRG and the slab SL preserved will complete the representation of the composite embedded structure 1611. FIG. 16D shows a cross-sectional view of composite embedded structure 1611 and shows areas of cutting media 1610 and surface relief structure 1608.

The representation of an IRG consisting of various 3D geometries may need to be converted to other representations for different purposes such as simulation and fabrication. Mesh-based representation can be achieved by converting various geometries into approximations consisting of triangular polygons using well-established tessellation methods. A voxel substrate representation can be constructed taking into account whether the center coordinates of each voxel lie within the geometry of the IRG. Based on these tests, the properties associated with the voxel can be set to those of the IRG material or the surrounding material.

How to modify the geometry of an interleaved rectangular grid

In some cases, it is useful to apply modifications to the geometric representation. These modifications may be appropriate to have a geometry that better matches the limitations of the manufacturing process or may be similar to that of the manufacturing process. The modification may be a mathematical transformation of the surface described by a mathematical formula, 2D and 3D geometric primitives, or a derived geometric mesh. Alternatively, the modification may be an algorithm that performs an analysis of the input geometry and computes a derived result based on this. Some modifications may be applied selectively to only part of the geometry of the IRG. Moreover, many modifications can be applied sequentially, as the input to one modification draws the geometric output from another modification. If the modifications represent fabrication processes, this approach can produce complex geometric features that are practically feasible with current fabrication methods. The modifications do not need to be applied to the entire IRG but can instead be applied to structures S1 and S2, or periodic structures PS1 and PS2 before constructing the IRG. Some examples of geometry modification methods are:

i) Linear coordinate transformation: i) Linear coordinate transformation: The transformation range of the system can be derived based on the linear transformation of coordinates. basically new The set of -coordinates can be derived from the input set of (x,y,z)-coordinates according to relation (156).

(156)

where M is the transformation matrix that fully describes the transformation, represents the transpose of a vector or matrix x. These transformations can be applied to the results of a mathematical function expression or to coordinates associated with a mesh representation. In particular, notable transformations include:

a. Scale transformation: Scaling the geometry in the x-, y-, and z- directions by factors of S _x , S _y , and S _{z ,} respectively, is achieved by the transformation matrix 157 .

(157)

b. Rotation about the z-axis: Counterclockwise rotation of the geometry about the z-axis by an angle γ is achieved by the transformation matrix (158).

(158)

Rotation in the x- and y-axes is also possible and can be associated with isolated structures, but is not suitable for application to the entire IRG due to the constraint that the lattice of the grid is parallel to the xy-plane. However, this rotation can be applied to structures S1 and S2.

c. Slant Modification: Figure 17A shows a perspective view of a single surface relief structure 1701, as an example of a single element of IRG. By applying a shift to the position of this structure as a function of height on the xy-plane, an inclined structure 1702 can be derived. This slope is achieved by the transformation matrix 159.

(159)

where α and β are the angles of inclination projected onto the xy- and yz- planes, respectively. In shown in Figure 17a, β=0. Skew operations within the xy-plane, or between the three coordinate axes, are also possible, but affect the IRG's grid vectors or make the grid's lattice no longer parallel to the xy-plane. However, these skew operations can be applied to structures S1 and S2.

series of linear transformations The composite action of can be calculated by multiplying the transformation matrices together.

(160)

Here M _tot is a complex transformation. In general, any transformation that affects the x- and y-coordinates, other than translation (which may depend on the z-coordinate), when applied to the entire grid, also transforms the IRG's grid vectors, which typically does the job. Change .

ii) Draft Modification - Figure 17b shows a perspective view of a single surface relief structure 1703, as an example of a single element of IRG. Modifying the draft involves adding a controlled taper to the faces of the model so that the walls become less steep and the size of the structure changes with height. A positive draft means the vertical walls taper so that the structure becomes smaller as the height increases, while a negative draft means the opposite. Structure 1704 shows the result of positive draft being applied to structure 1703 in a way that preserves the top shape of the structure. Similarly, structure 1705 is the result of positive draft being applied in a way that preserves the bottom shape of structure 1703, and structure 1706 is the result of the shape of structure 1703 at some midpoint between the top and bottom of the structure. This is the result of applying a positive draft in a way that preserves . Structure 1707 is the result of negative draft being applied in a way that preserves the top shape of structure 1703. Draft corrections can be selectively applied to the structure based on position or criteria, such as the gradient of the surface, prior to applying the draft (i.e., the corrections can be limited to being applied only to steep walls). Application of such drafts may be appropriate to better reveal the limitations of manufacturing processes, such as chemical etching followed by e-beam lithography, or to make the structure more suitable for mass-manufacturing. For example, using a positive draft on the sidewalls of the structure can aid release in molding processes such as injection molding or nanoimprint lithography.

iii) Blaze Modification - Figure 17C shows a perspective view of a single surface relief structure 1708 as an example of a single element of IRG. Structure 1709 shows the result of a blaze modification to structure 1708, where the top slope of the structure was modified by a specified and controlled angle. The application of blazes can affect the direction dependence of the diffraction efficiency of the grating, and thus can be advantageous for the optimization of designs that preferentially change the light distribution in various directions allowed by the grating equation.

iv) Rounding Modification - Figure 17D shows a perspective view of a single surface relief structure 1810 as an example of a single element of IRG. In , the sharp edges of the structure are replaced by rounded curves whose radius can be controlled. Structure 1711 shows a cross-sectional view of the result of applying rounding to the outer edges of structure 1710. Structure 1712 shows a cross-sectional view of the result of applying rounding to the inner edges of structure 1710. Structure 1713 shows the result of applying rounding to both the inner and outer edges of structure 1710. Depending on the process used to create the rounding, it may be appropriate to apply it selectively to only parts or structures, or to only two two-dimensional projections rather than all three dimensions. Figure 17E shows a top view of a pillar-shaped structure 1714 with a rectangular profile. Rounding in the xy-plane results in a modified structure 1715, which may nevertheless have a cross section that shows sharp changes when viewed in a projection including the z-axis. Rounding involves the fact that all manufacturing processes must have limits to the degree to which sharp edges can be reproduced. For example, nanoscale fabrication techniques have limits on the resolution of the features they can produce, meaning that edges are often significantly rounded at scales of <100 nm as a natural consequence of the resolution of the process. Modification processes can also introduce a controlled degree of rounding, for example, plasma processes can be configured to introduce a degree of rounding to preferentially erode sharp features. The form of the rounding itself can be described using a variety of curved geometries, including generally curved surfaces such as arc sections, sphere sections, cylindrical sections, or patches of suitably constructed NURBS surfaces. Rounding, sometimes referred to as filleting, is a widely available feature in many 3D modeling systems.

v) Undercut Modification - Undercut modification involves removing material from the part of the structure where the undercut is created, so that the structure is no longer a single value at the z position of all (x,y)-coordinates. Figure 17F shows a perspective view of a single surface relief structure 1716 as an example of a single element of IRG. By removing material from one side of the base of 1716, an undercut structure 1717 is created, which may result in advantageous properties for the direction, wavelength and polarization dependence of the light scattering properties of the diffraction grating.

vi) Inversion Modification - Figure 17g shows a perspective view of a single surface relief structure 1718 as an example of a single element of IRG. Inversion modification is defined here to mean exchanging the material designation of a structure within a certain height range with the surrounding material designation, which is usually air. Structure 1719 shows the result of applying an inversion modification to structure 1718, meaning that the pillars of structure 1817 become pockets 1720 within structure 1719. Many nanoscale fabrication processes involve a replication step in which a surface-relief imprint is made into a structure. Since these imprints are practical examples of inversion modifications, it is important to understand the role these modifications can have and how to account for them. For example, if mass production is to be replicated by a molding process from a master surface, the master surface must be an inverted modified version of the final surface. Although the periodic structures PS1 and PS2 that make up the IRG are characterized by the absence rather than the presence of material after inversion correction, the same symmetry rules governing whether the two-eye diffraction order of the IRG has non-zero efficiency apply. will be.

vii) Moth-Eye Modification - Figure 17h shows a cross-section of a single surface relief structure 1721 as an example of a single element of IRG. Moss-Eye modification involves adding small structures to the surface of an existing structure and then altering the optical properties of the entire structure. Often the additional structures are similar in shape. Structure 1722 is an example of a Moss-Eye modification, showing a cross-section of the result of adding a sharp, needle-shaped protuberance 1723 to structure 1721. Other modifications may include converting the Nassauscale's porous surface to another high-aspect ratio protrusion or a smooth outer surface. These structures can be created as part of a primary manufacturing process or by a secondary process such as plasma etching.

viii) Geometry morph modification - Figure 17i shows a pillar-shaped structure with a circular profile (1724) and a pillar-shaped structure with a rectangular profile (1725). 3D geometric morphing (also known as geometric transformation or mesh morphing) is the smooth transformation of the shape of one 3D object into another through warping and other distortion transformations. Shapes 1726, 1727, and 1728 illustrate various intermediate shapes that can be created with the morphing method. For simple shapes, this approach can be achieved within the parameters of a 3D geometric modeling system as previously described. For example, the structural profile 1724 is most easily described as a circle of diameter D, but it is formed by forming a square with side length D and then applying an edge rounding operation (also known as filleting) to all four corners. It may also be replaced by a 90° arc section with radius D/2. The profile 1725 of the structure is rectangular with a length W in the x-direction and a length H in the y-direction. An intermediate shape can be created by first constructing a rectangle with a rectangle having intermediate dimensions between the square profile used to construct the profile of the structure 1724 and the rectangular profile of the structure 1725. A corner rounding operation can then be applied to the four corners of this rectangle, with a radius between D/2 and 0 used to modify profile 1724 from square to round, as applied to the sharp corners of profile 1725. there is. Finally, extrusion operations can be used to create three-dimensional fillers. This protrusion will be the height between the two structures. The dimensions required for this process can be expressed parametrically. For example, assuming that γ is defined as a morph transition parameter that governs the degree to which one form is converted to another form, γ = 0 corresponds to structure 1724, and γ = 1 corresponds to structure 1725 ), and 0<γ<1 corresponds to an intermediate form that smoothly transitions between profiles. γ can then be used to interpolate between the dimensions required for the geometry construction operations described above: first, the length in the x-direction given by function (161) and then in the y-direction given by function (162). Constructs a rectangle with a length of

(161)

And the length in the y-direction given by the function

(162)

We then apply a corner rounding operation in which the corners of the rectangle are replaced by 90° arc-sections with a radius given by function (163).

(163)

Finally, a geometric compression operation must be applied to the form to the required height to create the filler form. If the height of structure 1724 is H ₁ and the height of structure 1725 is H ₂ , the height for the extrusion operation is given by (164).

(164)

Structures 1726, 1727, 1728 show the results of this approach used to convert between structures 1724 and 1725 for values γ = 0.25, 0.5, 0.75, respectively. It should be noted that this parameterization is only an example, and many others could be used, including switching different dimensions of the features at different rates (e.g. height is one form relative to the morph transition parameter rather than edge radius). can be converted from one form to another much more quickly). In particular, a variety of algorithms are available in the computational literature to compute morphed geometries between more complex shapes, as these methods have attracted considerable interest in the filmmaking and videogame industries over the years. do. Mocanu's doctoral thesis "3D Mesh Morphing" (Pierre and Marie Curie University, 2012) provides a review of various methods. Because many algorithms rely on mesh geometry, it may be necessary to convert the shape of the morph's end-points to a geometrically equivalent mesh representation. Some algorithms rely on user interaction to identify features or regions that would be commonly associated by a morph, while other methods attempt to do this automatically. For practical applications, care must be taken to ensure that intermediate forms are feasible for the intended manufacturing method. To ensure this, modifications to the shapes created by complex morphs may be necessary. Additionally, morphing methods can be used iteratively and continuously. For example, an intermediate form between a first form and a second form can be created, and this form can then be manipulated to calculate a new morph between the first or second form and the manipulated intermediate form.

In many cases, creating a representation of these modifications requires conversion to a mesh representation rather than a mathematical function. This is especially true for transformations that render the surface no longer a single value in the z-direction. Additionally, it is understood by those skilled in the art that these modification methods are merely examples of a wide range of techniques for manipulating and modifying geometry as evidenced by 3D computer-aided design and 3D computer graphics systems as well as modeling tools provided in the academic literature. It will be.

Method for modifying interleaved rectangular grids by application of single or multiple coating layers

Another form of modification to IRGs consisting of surface relief structures, both in terms of geometrical representation and as an actual step in manufacturing devices in the physical world, is to apply one or more coatings over the grating surface. It has been found that by providing a thin-film of a discrete material over the surface relief structure, advantageous performance advantages can be obtained. One advantage of this approach is that it allows the use of materials with high refractive indices that would otherwise not be available for the fabrication of nanostructured surface relief geometries. The use of high index materials not only brings beneficial advantages in the magnitude of the diffraction efficiency of various non-zero diffraction orders, but can also provide additional degrees of freedom for the design and optimization of the IRG.

There are various techniques in the coating process that can be used depending on the requirements, and these may give different results on the resulting structure.

In one approach, material may be added over the surface relief structure in the z-direction. FIG. 18A shows a cross-sectional view of an IRG with a portion of the surface relief structure 1801 of the IRG. By adding material in the z-direction, a coating layer 1802 is introduced over the structure forming composite structure 1083. A practical approach to achieve such directional coatings is to use physical vapor deposition (PVD), which consists of a well-collimated beam and the xy-plane of the grid placed perpendicular to the direction of the coating vapor.

Instead, the directional coating may be applied in a direction oblique from the normal to the surface. 18B shows a surface where a deposition vapor 1805 is applied in a tilted direction from the normal of the grid, resulting in a directional build-up of the coating material 1806, including a shadowing effect. A cross-sectional view of the IRG with relief structure 1804 is shown. This coating may be achieved with methods such as PVD, by tilting the plane of the gratings so that the coating direction matches the design intent.

In another approach the coating can be applied to the IRG conformal in all directions, meaning that the thickness is as equal as possible. 18C shows a cross-sectional view of an IRG with a surface relief structure 1807 thereon, a conformal coating having the same thickness, as measured in the direction perpendicular to the surface, at all points on the surface except the inner corners of the surface. (1808) applies. These coatings can be applied using methods such as atomic layer deposition, or by rotating the coating over a wide range of tilt angles relative to the PVD source, depending on the geometry of the coating and potential shading effects.

By varying, or otherwise varying, the tilt of the grating relative to the directional coating source, it is possible to form a coating that is an intermediate condition between these various cases. For example, extreme directional changes in the thickness of coating 1806 may not be desired. Instead, the tilt of the lattice surface is dynamically varied during the coating deposition process, and the time spent at a given tilt angle affects the rate of coating formation on the surface at this angle, so that a defined thickness of material is applied to the various sides of the structure 1804. Please note that accumulation in fields can be guaranteed.

Coatings can be sequentially applied to various materials to further modify the scattering properties of the IRG. Figure 18d shows a cross-sectional view of an IRG with a surface relief structure 1809, on which a first coating layer 1810 is applied, and a second coating layer 1811 is applied thereon. This layer then has a third coating layer 1812 applied thereon. In principle, the coating process of each layer can be different, which means that successive coating layers can be variably directional, conformal or intermediate between the two, as well as have different thicknesses and materials. . In this way, complex modifications of the base surface relief structure can bring additional degrees of freedom for the design and optimization of the scattering properties of the IRG.

Geometrical representations of coatings can be created by a number of methods. In general, this results in a surface geometric representation for each layer of material. For a mathematically-based description, the derived geometry for the coating can be generated by calculating the derivative based on existing surface functions. First, the IRG coating surface function is It is assumed that, where i is an index representing the coating layer of a system with two or more coatings. For a coating applied in the z-direction where the th layer has a thickness of t _i , the corresponding IRG coating surface function is given by (165).

(165)

For coatings applied in different directions, the offset surfaces may intersect themselves or intersect the base geometry, making it difficult to use general representations. However, these geometries can be found using numerical algorithms that use a mesh-based representation of the surface. Additionally, for the IRG surface function where x- and y-direction gradients can be evaluated, the surface function for the oriented coating of the ith layer is the coating offset in the z-direction at the given (x,y)-coordinates. This can be schematically described by projection, leading to the definition of the IRG coating surface function (166).

(166)

where the IRG surface function underlying the 0th layer of the coating Define it as, is defined as a function of the coating direction and is the normalized surface normal vector. and is a function of the normalized coating direction vector V. Here, the normalized surface normal vector is given by (167).

(167)

For the convention that the surface relief structure protrudes in the +z direction and the coating direction points towards the surface from +z, a simple description of the coating direction function ensures that coating is possible only within an angle of ±90° with respect to the coating direction vector V. The definition is given as (168),

(168)

here, silver vector and It is the dot product of .

In general, the approach specified by equations (166) to (168) will reach its limits for all but very thin coatings. For thick coatings, appropriate surfaces can be derived based on 2D and 3D geometry primitives, where each coating layer, including the primitive structure, is represented by its own mesh or a composite of 2D and 3D primitives. do. For these representations, well-established methods can be used to generate derived geometries using offsets defined according to coating rules. Methods can then be used to check these derived geometries for self-intersecting features, or for interference with the base geometry and appropriate cutting and stitching methods used to create a valid geometric representation of the coating surface. there is.

Practical realization of coatings often presents more complex effects in the thickness of the coating across the surface, as well as variations in the composition and properties of the coating. These effects can be achieved through the use of rounded corners to represent in-fill that can occur at interior corners, or by using ray tracing and shadow casting methods to represent line-of-sight changes in coating thickness. This can be captured in a representation through the use of appropriate modifiers to the geometry, such as ray tracing methods.

Method for construction of a rectangular grid interleaved from multiple layers of structures and coatings

The application of coating layers is one approach to introduce various new materials into grids. Another approach is to apply a new layer of structure. 19A shows a cross-sectional view of a grating with a surface relief structure 1901 made of a first material (M1), a cross-sectional view of a grating with a surface relief structure 1902 made of a second material (M2) and a third material (M3). ) shows a cross-sectional view of a grid with a surface relief structure 1903 consisting of ). By applying structure 1903 followed by structure 1901 and structure 1902 on a substrate, a new multilayer lattice, which may be an IRG, is formed into a surface relief structure 1904 composed of the materials of structures 1901, 1902, and 1903. is created with

In this approach, a representation of this geometry can be created by simple addition of surface functions. for example, is the IRG surface function of this structure (1901), If this is the IRG surface function of the structure 1902, and t ₃ is the thickness of the base layer, the following surface geometry function can be defined for the layers of the multilayer IRG.

(169)

Alternatively, a mesh-based representation of the geometry may include a plurality of meshes where the meshes of each layer except the first layer are created by taking the sum of the z-positions of the meshes of the previous layers. If the meshes have the same (x,y)-coordinates for the vertices of the polygons that make up each mesh, then the sum of the z-positions of the meshes of the layers is calculated to calculate the mesh for the derived layer. Just doing it is enough. Typically, this overlap of the (x,y)-coordinates of the vertices of different meshes is not guaranteed, so instead it may be necessary to subdivide the polygons of each mesh layer until this condition is achieved.

When combining layers of surface geometry, such as meshes, where at least part of the geometry is single-valued in the z-direction, care must be taken to handle intersections between mesh layers if they occur. When this situation occurs, various methods can be used. One way is to use a trimming operation to remove parts of the geometry based on a method of assigning priorities between the geometries, such as selecting materials with priority. Prioritization of materials can be achieved by taking into account the manufacturing process in which the materials are prioritized in the order in which they are deposited, such that the first material deposited on the substrate has priority over the second material deposited.

An approach based on 3D geometry that describes a closed volume can proceed by overlapping different geometries with respect to each other and adopting rules governing the overlap area. As with surface geometry, one rule may be to assign priorities between different materials, with a given material in overlapping areas being set to the higher priority material.

Another approach for multilayer lattices is to encapsulate the structure in different, discrete layers of surrounding material, and the various methods described above for representing and modifying the geometry can be used for each layer of material. This can allow the creation of complex multi-layer geometries for lattices that can be IRGs. For example, Figure 19B shows a planar base layer 1906 of first material (M1); a first periodic IRG structure 1907 comprised of a second material (M2) disposed on a base layer 1906; a medium 1908 comprised of a third material (M3) surrounding structure 1907 and forming a new planar layer 1909 on top of structure 1907; a second periodic IRG structure 1910 composed of a fourth material (M4) disposed on a planar layer 1090; A medium 1991 composed of a fifth material (M5) surrounding the structure 1910 and forming a new planar layer 1912 on top of the structure 1910, and a medium surrounding the lattice, identical to the planar base layer 1906. It shows a cross-sectional view of a portion of a multilayer IRG 1905 comprised of a medium 1913, which may be a medium or a sixth material (M6). Those skilled in the art will understand that additional layers may be added to provide additional freedom for design.

It should be noted that in a multilayer IRG, each layer of periodic structures must be an IRG, a rectangular grid, or a 1D grid. For all layers with a 2D grid, the various layers must have the same grid vectors. Layers with a 1D grid must have a grid vector equal to one of the grid vectors of the 2D grid layers, the sum of the grid vectors of the 2D grid layers, or the difference of the grid vectors of the 2D grid layers. Otherwise, new grating vectors are introduced, resulting in additional scattering directions for each beam, which may cause failure of the IRG's image relay function. For some layers, there is a significant possibility that the structure S1 or S2 of the IRG is null, equivalent to a rectangular grid. Additionally, the position of each layer's lattice can be shifted relative to the others. It should be noted that coherent scattering effects may only be possible in multilayer systems where the optical path length through the system is shorter than the coherent length of the light source used with the system. Grating layers separated by more than a coherence length can be considered independent of each other and are processed separately for calculation of scattering properties such as diffraction efficiency.

In a multilayer representation, where systems with coatings are included in the definition of a multilayer system, the assignment of the material and its properties can proceed, with some modifications, in a manner similar to that described for single-layer structures. In one approach, each surface is assigned a material index and a priority index. The priority index may be based on considerations of the intended manufacturing method, and surface geometries are given priority based on the order in which they are manufactured. The material designation at the coordinates (x, y, z) is then determined by finding the highest priority surface that this point lies below (or within, in the case of encapsulated geometries). In this way, descriptions such as voxel substrate representations can be realized from representations of the geometry of multilayer IRGs composed of different materials.

Design and representation method of interleaved rectangular grids based on mathematical description of volume properties

The use of representations based on surface geometry is well suited to IRGs based on separate materials with different morphologies. In other embodiments of the invention, variations of one or more optical properties within the material region of the IRG may be constructed. For example, periodic changes in the orientation pattern of birefringent materials, such as liquid crystals, can be created and provide grating structures with particular sensitivity to the polarization of the incident light beam.

Instead of representing the grid in terms of the geometry of structures made of different materials, an alternative approach is to describe the optical properties of the volume containing the IRG directly in terms of position coordinates. One approach, like IRG's volumetric description, consists of the following steps:

One. Assume that the plane of the grid is the xy-plane and is at z=0. The lattice vectors used to construct the lattices (L1, L2) of the IRG are defined as (170) and (171).

(170)

and

(171)

2. To describe the finite range of the IRG, a cropping function C(x,y) is defined. C(x,y) has the value of 1 in the area where the grid exists, and has the value of 0 in all other areas. Therefore, if cropping is not needed, C(x,y)=1 regardless of the (x,y)-coordinates.

3. Lattice L1 is expressed as the lattice function L_1 (x,y) given by (172),

(172)

Lattice L2 is the lattice function given by (173) It is expressed as

(173)

here, is the grid offset vector.

4. Volumetric property function as an expression of the optical properties of the structure S1 of IRG. defines , which essentially explains how S1 introduces some modifications to the surrounding medium. Similarly, we define the volume characteristic function N ₂ (x,y,z) as a representation of the optical properties of the structure S2 of the IRG. The properties described by the volume characteristic function may be any physical quantity associated with the representation of the lattice, including, but not limited to, refractive index, electrical permittivity, permeability, birefringence, absorptivity, or exponent values indicative of material composition. Each function N ₁ (x,y,z) and N ₂ (x,y,z) is a mathematical function, a three-dimensional grid of values combined with an interpolation scheme, or (x,y,z)-coordinate input. Another approach could be that unique feature values can be generated based on The finite range of the characteristics of structures S1 and S2 is the respective volume property function, which may be a null value or a number with a special meaning sufficiently distinct from the range of numerical values necessary to describe the corresponding range of optical property values. can be expressed by defining special values of N ₁ (x,y,z) and N ₂ (x,y,z). In the x- and y-directions, N ₁ (x,y,z) and N ₂ (x,y,z) are both defined entirely within a rectangular region of the same dimensions as the IRG unit cell. Likewise, N ₁ (x,y,z) and N ₂ (x,y,z) are defined to have non-zero values only for rectangular regions in the xy-plane of the same size and orientation as the IRG unit cell. Typically, this area is centered at the origin (0,0), but this does not have to be the case. Volume property functions may include areas within an undefined unit cell. This can be useful when considering how structures will overlap when constructing an IRG. One way to indicate lack of definition is to use a specially assigned value ξ, which must be taken into account when joining structures together.

The periodic structure of IRG, PS1, is a volume characteristic function and lattice function It is expressed as a periodic volume characteristic function P ₁ (x,y,z), defined as a three-dimensional convolution of and given by (174).

(174)

Similarly, the periodic structure PS2 can be expressed as a periodic volume characteristic function (175).

(175)

The convolution of equations (174) and (175) can be expanded to (176) and (177).

(176)

and

(177)

6. IRG is constructed by combining PS1 and PS2 together, and is expressed as the IRG volume function I(x,y,z). This function describes the change in a given optical property as a (x,y,z)-coordinate function. The process of combining periodic structure functions P ₁ (x,y,z) and P ₂ (x,y,z) together not only has to take into account possible regions where the function is assumed to be absent, but also requires consideration of possible regions where the structure will be embedded in the surrounding medium. It should be noted that this can happen. Periodic structure functions P ₁ (x,y,z) and P ₂ (x,y,z) are volumetric characteristic functions in such a way that the absence of a feature in the (x,y,z)-coordinate is indicated by a specially specified value ξ It can be defined using . In this case, a masking function (187) is defined for the periodic structure PS1, a masking function (179) is defined for the periodic structure PS2,

(178)

For periodic structure PS1

(179)

For periodic structure PS2

(180)

The region where the periodic structure functions P ₁ (x,y,z) and P ₂ (x,y,z) overlap requires some methods to describe the properties described by each periodic structure. One way to control this overlap is by defining a combiner function X(a,b), which can be composed of various expressions depending on the requirements and intent of the expression. The definitions of possible functions given in equations (134) to (142) are also valid for volume expression. Using the masking function and the selected combiner function, and noting that the medium surrounding the IRG is defined to have a characteristic value of P ₀ , the IRG volume function for the required properties can be written as (181).

(181)

This completes the expression of the IRG using the volume function.

For clarity, single-valued scalar functions are defined here for the properties of the IRG and the corresponding contributions from S1 and S2. It will be clear to those skilled in the art that this definition can be generalized to many separate functions that follow the same general scheme but each describe a different characteristic of the volume. This way, the overall characteristics of the volume can be described. This can include tensor properties such as the electric permittivity tensor required for anisotropic media such as liquid crystals, since every tensor can be composed of a sufficient number of scalar values. Alternatively, by providing a volumetric description of the index values corresponding to the material selection, the optical properties at a given point can be determined by finding the material index at the given (x,y,z)-coordinates and then consulting a table that provides the optical properties of the material. It can be decided by doing this.

The use of volumetric representation is advantageous for design and simulation by directly expressing the three-dimensional changes in properties necessary to understand the response of IRGs to electromagnetic radiation. Conversion to data associated with a voxel-based representation or three-dimensional mesh, required for many simulation approaches such as RCWA or FDTD, can be achieved simply by evaluating the IRG volume function at each voxel centroid coordinate or mesh-node. . The volumetric approach is also well suited to representing systems in IRG where the optical properties of the material can vary with position. Examples of such systems include systems that rely on changes in the alignment of liquid crystal molecules or phase change polymers, including specific optical polymers, as well as specific metamaterials.

In some practical applications, conversion between volume and surface geometry representations may be advantageous. The conversion from a surface geometry representation to a volume representation can be accomplished in a manner similar to that used in the construction of the voxel-to-substrate representation. The IRG volume function at a given (x,y,z)-coordinate can be evaluated by using surface geometry data to determine the material at that point in space and referencing the required optical properties from a look-up table associated with the material. there is. The change from a volume representation to a surface geometry representation requires that the optical properties described in the volume description match the available materials. Calculation of surface geometry can be achieved by finding the edges of three-dimensional regions with identical properties (potentially within a tolerance threshold). This is an example of an isosurface calculation for which a variety of well-established methods exist as well as support in various software packages, such as the isosurface function provided as part of the Matlab® language (MathWorks, Inc.). Constructing surface geometry from volume data is particularly important for the fabrication of surface relief IRGs, which require three-dimensional geometry for tooling fabrication, such as mastering tools.

How to Make a Difference in an Interleaved Rectangular Grid

As detailed previously, in order for the IRG to have a non-zero two-eye diffraction order and to be able to use the output coupled waveguide light for observation, some method for symmetry breaking must be used. Figures 20A-20J show examples of various methods for engineering differences between the periodic structures PS1 and PS2 of the IRG. In all cases, the structures are displayed as surface relief structures or profiles in a top down view, but the methods described can be used to create embedded structures, structures composed of several materials or multilayers, and volumetric changes in material properties. The same will apply to the structures being created. Additionally, in all cases, it is assumed that the structures may be composed of a material with at least one optical property that is different from their environments and therefore will scatter light. The methods shown in Figures 20A-20J are identified as follows:

a) Scale difference: Figure 20a shows a plan view of part of IRG (2001). Here the structures S1(2002) and S2(2003) are the same, and the lattice offset vector is , which means that IRG (2001) is FSIRG. Increase the size of structure S1(2002) as seen in the x-plane to form a new structure S1(2004), and increase the size of structure S2(2003) as seen in the xy-plane to form a new structure S2(2005). By reducing , a modified IRG (2006) is created. Due to the breaking of shape symmetry due to scale changes, this new IRG (2006) may have two-eye orders with non-zero diffraction efficiencies, the magnitude of which is expected to depend on the scale difference between structures S1 and S2. do. Alternatively, this scaling may be applied to only one of the structures, either along a single direction of the xy-plane or by different amounts along both directions of the xy-plane.

b) Relative lattice shift - Figure 20b shows a top view of part of IRG (2007). where the structures S1(2008) and S2(2009) are the same and the lattice offset vector is the vector , which means that IRG (2007) is FSIRG. By changing the lattice offset vector to shift lattices L1 and L2 relative to each other, copies of structures S2 (2010) will be moved closer to some of the closest copies of structures S1 (2008). You can. In this example the shift in the y-direction is shown. Due to the breaking of position symmetry, this new IRG (2011) has non-zero two-eye orders, the size of which depends on the size and direction of the relative lattice shift.

c) Rotation difference - Figure 20c shows a top view of part of IRG (2012). where the structures S1(2008) and S2(2009) are the same and the lattice offset vector is the vector , which means that IRG (2007) is FSIRG. Rotate structure S1(2013) clockwise around the z-axis to form the new structure S1(2015), and rotate structure S2(2014) counterclockwise around the z-axis to form the new structure S2(2016). By rotating in orientation, the modified IRG (2017) is generated. Due to the breaking of shape symmetry by rotation, this new IRG (2017) can have non-zero diffraction efficiencies of two-eye orders, the magnitude of which generally depends on the rotation angle applied to structures S1 and S2. . Alternatively, rotation can be applied only to structures S1 or S2.

d) Mirror difference - Figure 20d is a top view of part of IRG (2018). where the structures S1(2008) and S2(2009) are the same and the lattice offset vector is the vector , which means that IRG (2007) is FSIRG. By mirroring structure S2 (2019) about the yz plane to form a new structure S2 (2021), the modified IRG (2022) is generated. Due to the breaking of shape symmetry by mirroring, the new IRG (2022) may have two-eye orders with non-zero diffraction efficiency. Unlike other operations, mirroring cannot be applied incrementally; the only choice is which plane the structures are mirrored in and which structures are selected for mirroring.

e) Height difference - Figure 20e shows a perspective view of part of IRG (2023). where the structures S1(2008) and S2(2009) are the same and the lattice offset vector is the vector , which means that IRG (2007) is FSIRG. By increasing the height of structure S1 (2024) to form a new structure S1 (2026) and decreasing the height of structure S2 (2025) to form a new structure S2 (2028), a modified IRG (2028) is created. do. Due to the breaking of shape symmetry by changing the height, the new IRG (2028) can have two-eye orders with non-zero diffraction efficiency, the magnitude of which depends on the difference in height introduced between the structures S1 and S2. It is expected to change. Alternatively, the change in height may apply to only one set of structures.

f) Blaze difference - Figure 20f shows a perspective view of part of IRG (2029). where the structures S1(2008) and S2(2009) are the same and the lattice offset vector is the vector , which means that IRG (2007) is FSIRG. The structures show sloped tops due to blaze modifications. By increasing the blaze angle of structure S1 (2030) to form a new structure S1 (2032) and decreasing the blaze angle of structure S2 (2031) to form a new structure S2 (2033), the modified IRG (2034) is created. Due to the breaking of the shape symmetry by the change of the blade, this new IRG (2034) may have two-eye orders with non-zero diffraction efficiency, the magnitude of which depends on the change of the blaze angle applied to the structures S1 and S2. It is expected to vary depending on. Alternatively, changes in the blaze may apply to only one of the structures, or may include changes in slope orientation.

g) Shape difference - Figure 20g shows a top view of part of IRG (2035). where the structures S1(2036) and S2(2037) are the same, and the lattice offset vector is , which means that IRG (2035) is FSIRG. By changing the shape of structure S2 3037 from a circular profile to a square profile 2038, a modified IRG 2039 is created. Due to the breaking of the conformational symmetry in this change, the new IRG (2039) may have two-eye orders with non-zero diffraction efficiencies, the magnitude of which will depend on the similarity of shape to the structures S1 and S2. It is expected. Geometric morphing methods can be used to create a range of shapes with controllable differences. For example, two forms can be used to represent the possibility of two extreme forms, from which the morph is used to calculate an intermediate form that could be used in the IRG. If the morph is smooth and continuous, it is in principle possible to create forms with successive degrees of difference from each other, providing a wide range of geometrical variations. Except for relative lattice shifts, all of the methods listed above can be considered examples of shape differences that are built on a specific aspect, such as height or rotation.

h) Optical properties difference - Figure 20h shows a top view of a portion of IRG (2040). where the structures S1(2008) and S2(2009) are the same and the lattice offset vector is the vector , which means that IRG (2007) is FSIRG. By changing the composition of structure S2 (2042) to form structure S2 (2043), a modified IRG (2044) is generated such that at least one intrinsic optical property differs from S1 (2040). . Due to the breaking of compositional symmetry, this new IRG (2044) may have two-eye orders with non-zero diffraction efficiencies, the magnitude of which is expected to depend on the degree of difference in the optical properties of structures S1 and S2. do.

i) Splitting and merging of structures - Figure 20i shows a top view of a portion of IRG 2045. where the structures S1(2008) and S2(2009) are the same and the lattice offset vector is the vector , which means that IRG (2007) is FSIRG. By replacing structure S2 (2047) with a new structure (2048) composed of multiple elements, a modified IRG (2049) is created. Due to the breaking of shape symmetry, the new IRG 2049 may have two-eye orders with non-zero diffraction efficiency. In addition to splitting a structure into multiple elements, the structures can also be merged together. In fact, all of these changes can be viewed in the form of geometric morphs, on the basis of which several intermediate structures can be created to provide a wide range of morphological symmetry breaking. For example, Figure 20j shows a top view of a single structure 2050. This structure can be elongated to form a new structure 2051. By narrowing the center of structure 2051, a shape 2052 can be created that appears to be two elements fused together. By narrowing the waist between the structures to the point where the elements are separated, a new structure 2053 consisting of two elements 2054 and 2055 can be formed. Accordingly, structures 2051 and 2052 can be considered intermediate structures within the range of structures between structures 2050 and 2053.

It should be noted that when applying an IRG as part of a DWC, it is desirable that differences created in the IRG using the method described above or other methods do not alter the periodicity or orientation of the lattices L1 and L2 of the IRG. This changes the directions of the various diffraction orders and can interfere with the function of the IRG in DWC. The methods described above can be applied individually or combined together and even repeated several times. In principle, any of the shape modification methods previously identified can be used to create symmetry breaking, including draft correction, slope correction, rounding, as well as single and multilayer coating methods. Accordingly, the modifications described in detail above should be considered examples of a wide variety of modifications. For example, all modifications to the geometry can in principle be applied only to structure S1 and/or periodic structure PS1, or only to structure S2 and/or periodic structure PS2. Alternatively, geometry modifications may be applied to both sets of structures, but to different degrees. For example, the two periodic structures PS1 and PS2 in the IRG will undergo tilt modification with symmetry breaking achieved by changing the magnitude and/or direction of the tilt applied to the periodic structure PS1 compared to applying it to the periodic structure PS2. You can.

It will be appreciated that these modifiers do not need to use the FSIRG as a starting point, and that differences between the underlying periodic structures can be used to augment an already existing IRG. It is also important to note that the method of deriving the difference between the periodic structures PS1 and PS2 described above is only a sample of the various possible modifications that enable the described advantages for controlling the diffraction efficiency of the diffraction order of the IRG. do.

Use of interleaved rectangular gratings using diffractive waveguide couplers

Figures 21A and 21B show a perspective view and a plan view, respectively, of a layout for an augmented reality display system including a diffractive waveguide coupler employing an embodiment of an interleaved rectangular grid. The diffractive waveguide coupler 2101 consists of an optically transparent substrate 2103 composed of planar slab waveguides, an input grating 2104, and an output grating 2105 composed of interleaved rectangular gratings. The medium (M) surrounding the DWC (2101) has a smaller refractive index than the substrate (2103). Typically, this medium will be air, but it does not need to be. The medium M is usually the same on all sides of the waveguide, but this need not be the case. In general, the thickness of the substrate 2013 may be 0.1 mm to 4.0 mn, and preferably 0.25 mm to 1.0 mm. The external profile of the substrate 2013 in the xy-plane is shown as a rectangle in FIG. 21, but the input grid 2104 and IRG 2105 will be of the size required to receive output from the projector 2102 and the design eyebox of the system. If possible, this could be in a broad form.

The waveguide surfaces of the substrate 2103 have very low roughness, as well as high flatness and parallelism with respect to each other. The non-guided sides of the substrate 2103 may be painted black or treated with a light absorbing material, and the scattering of light incident on the non-guided sides may affect the performance of the DWC 2101 by introducing artifacts such as haze. It may have a rough or smooth surface finish to reduce returning to the waveguide.

Viewing real-world light through the guiding surface of DWC 2101 is possible, due to the light transmission properties of substrate 2103 and the real-world light incident on DWC 2101 from the surrounding medium M. This is due to the existence of the 0th diffraction order of IRG, which has a non-zero diffraction efficiency for . In other configurations where it is not necessary to view real-world light, a light occlusion device may be used on the opposite side of DWC 2101, where the occlusion device ensures that light from the real-world does not interfere with viewing the projected image. It is composed.

Projector 2102 is configured to generate an ensemble of collimated light beams directed to fall directly on input grating 2104. The output of projector 2102 can be monochromatic or cover a variety of wavelengths to provide a full color image. The ensemble of light beams forms an image focused at infinity, which will be displayed by DWC 2101 with viewing the real-world light transparently through DWC 2101. The light beam from projector 2101 is coupled to DWC 2101 by input grating 2104 using the methods described herein and undergoes waveguide propagation toward IRG 2105, where it undergoes waveguide propagation for eyebox expansion. Both pupil replication and output coupling for observation occur by the repetitive interaction of the IRG 2105 and the light beam as a result of the diffractive scattering properties of the grating.

Typically, the output beam of projector 2102 is circular and has a diameter of 0.25 mm to 10 mm, and preferably 1.0 mm to 6.0 mm. The ensemble of beams output from the projector 2102 will have a range of xy-wave vectors. For projectors based on rectangular microdisplays such as LCOS, DMD or micro-LED display panels, the extent of the xy-wavevector typically consists of an approximately rectangular region in k-space. Although different light projection techniques may produce different shapes, the display system of projector 2102 that produces an image with a non-zero viewing field of view produces a range of xy-wavevectors that correspond to at least one region of k-space. .

In some applications, an observer (not shown) may see light coupled out from IRG 2105. In some arrangements, the observer will be on the same side of the projector 2102 and DWC 2101, and in other arrangements the observer will be on a different side of DWC 2101.

The planes of the input grating 2104 and the IRG 2105 are configured to be parallel to the guiding surfaces of the substrate 2103. Cartesian (x,y,z)-coordinates are defined, with the xy-plane parallel to the diffraction grating and the guiding planes of DWC 2101. Both the input grating 2104 and the IRG 2105 may be located on one of the outer guiding surfaces of the substrate 2103 or may be embedded within the substrate. Input grating 2104 and IRG 2105 do not need to be in the same plane, but must be parallel to each other. Input grating 2104 and IRG 2105 may be comprised of grating vectors advantageous for operation as a diffractive waveguide coupler for augmented or virtual reality display applications. Accordingly, the notable cumulative orders and nomenclature in Tables 1 and 2 may be adopted to facilitate description of the operation of DWC 2101.

The input grating 2104 has a structure and composition suitable for diffraction scattering of light and is a one-dimensional grating with a grating vector given by (182).

(182)

The period of the input grating p _y is such that first-order diffraction scattering of the light beam from the projector 2102 generates a light beam that is guided within the substrate 2103 by total internal reflection. It has been confirmed that in many applications, p _y may preferably range from 150 nm to 800 nm, and for applications using visible light, it may be desirable to range from 250 nm to 600 nm.

Depending on the range of wavelengths output by the projector and the refractive index of the substrate 2103, finding the value of p _y at which all xy-wave vectors will be within the waveguide range of the substrate 2103 after first-order diffraction by the input grating 2104. It may be impossible. In this case, the designer can select the combined viewing field of view and display wavelength such that the range of xy-wavevectors is accommodated within the guiding area of DWC 2101 or selected portions thereof.

If the substrate 2103 has a refractive index n, the medium M has a refractive index n ₀ , and λ ₁ and λ ₂ are, respectively, the shortest and longest wavelengths in vacuum in the range required for display by DWC 2101, then the entire observation To enable TIR guidance over the entire field of view and wavelength, p _y must satisfy the following inequalities to enable TIR guidance across the entire field of view and wavelength:

(183)

and

(184)

here, and are the horizontal and vertical viewing fields of view of the display in medium M, respectively, where is defined taking into account the angle subtended by the range of the wave vector when projected onto the xy-plane, is defined by considering the angle substituting the range of the wave vector projected onto the yz-plane. Here, it is assumed that the beam corresponding to the center of the observation field is incident perpendicularly to the planar input grid 2104. It will be clear to those skilled in the art that other arrangements are possible where the projector 2102 is tilted so that the center of the field of view is not normal to the plane of the input grating 2104, in which case equations (183) and (184) should be adjusted accordingly.

In some systems, it is advantageous for the available area of k-space available for waveguiding by TIR to be less than the limits enforced by TIR and evanescence. One reason for doing this is to ensure that the distance between successive pupil copies remains within the desired range, as predicted by equation (85). This situation is the xy-wave vector of the waveguide light in DWC (2101) can be considered by defining a cropped waveguide region that satisfies (185).

(185)

Here, the parameter f ₁ increases the minimum angle of incidence of the guided light beam on the surface of the DWC 2101 compared to the TIR limit, and the parameter f ₂ reduces the maximum angle of incidence of the guided light beam on the surface of the DWC at the limit of 90°. Parameters f ₁ and f ₂ must satisfy inequality (186).

and (186)

To constrain the viewing field of view to fit within the cropped waveguide region of equation (185), p _y needs to satisfy inequalities (187) and (188) below.

(187)

and

(188)

If these inequalities cannot be satisfied simultaneously, the combined range of wavelength and viewing field of view is much larger compared to the cropped waveguide area of substrate 2103.

Typically, the input grating 2104 should be, but need not be, large enough to receive the entire ensemble of beams from the projector 2102 so that no light from the projector is wasted. In principle, light can be coupled to the waveguide region in k-space by the input grating 2104 via both diffraction orders of m ₁ =+1 and m ₁ =-1. This causes the ensemble of light beams to move in both the common +y and -y-directions. For purposes of DCW 2101 only the +y-direction is preferred. As such, the input grating 2104 has a diffraction efficiency of the order m ₁ =+1 that is much larger than the diffraction efficiency of the order m ₁ =-1 over the range of incident beam angles and wavelengths provided by the projected light. The structure and composition of the cell can be characterized. This can help increase the overall optical efficiency of DWC 2101.

The IRG 2105 may be positioned such that the center of the grid lies approximately in the +y-direction with respect to the center of the input input grid 2104. The lattice L1 and L2 of IRG 2105 are composed of lattice vectors (189) and (190).

(189)

and

(190)

Here, the period p _y in the y-direction is set equal to the period of the input grid 2104. The period _p It may be chosen to continue to undergo guided propagation within the substrate 2103 after undergoing a T+X to TX transition order as defined in Table 2 of 70. In some embodiments, guided beams corresponding to beams _from projector 2102 with an initially positive _k It is advantageous to ensure that the guided beams corresponding to the beams from ) remain guided even after the T+X transition order. This is to ensure advantageous coverage of the eye box by ensuring that the light beams moving in the +x direction after output are distributed to the -x side of the DWC (2101) based on the center of the input beam position. Likewise, after output -x This is to ensure that light beams moving in this direction are distributed to the -x side of the DWC (2101). This may provide a better perspective for ensuring that the projected eyebox of the beam moving in the ±x-direction after output is covered by appropriate pupil replication events. Assuming that this condition is guaranteed and that the cropped waveguide region described by inequality (185) applies, p _x must satisfy the inequalities (191) and (192) below.

(191)

and

(192)

In most cases, p _x is It is desirable to be in the range of .

The IRG 2105 is capable of providing enough space to cover the intended size of the system's eyebox, including considering the projection of the eyebox for all points in the viewing field of view from the defined location to the plane of the IRG 2105. It should be large enough to provide pupil replication. If the central ray exits DWC 2101 with incidence perpendicular to the surface, the size of the eyebox located at a normal distance from the waveguide is w in the x-direction and h in the y-direction of the IRG 2105. The size must satisfy (193) in the x-direction and (194) in the y-direction.

(193)

in x-direction

(194)

In the y-direction. where _dp is the diameter of the entrance pupil of the system used to observe the output from the grid, and the output grid is in principle sized such that the entrance pupil can be filled at all positions within the eyebox. In some configurations, the pupil arising from light beams along a path characterized by a cumulative order of {±1, -1} of the IRG with only a single T+X or TX transition order and no other transition orders before the beam is output. It is advantageous to ensure that the eyebox is covered. This requires that the output grid dimensions in the y-direction be increased at each end by a distance depending on the intended layout of the input grid 2104 and IRG 2105, which corresponds to the longest and shortest wavelengths intended for the design. It can be calculated in a simple way by analytical or computational ray tracing of the field of view with respect to wavelength.

The relationship of (183), (184), (187), (188), (191), (192), (193) and (194) is a rectangular viewing field of view facing the x- and y-directions of DWC 2101. It is effective in and causes the center of the observation field to be perpendicular to the DWC (2101). Other _shapes and orientations of the viewing field of _view are _possible if the grid periods _p ), or can be derived through geometric ray tracing of the eyebox for the size of the IRG (2105).

The structure of IRG 2105 may be comprised of one or more materials, including a surface relief structure, a surface relief structure with one or more coating layers, an embedded structure, an embedded structure with one or more coating layers, a multilayer surface relief structure, It may be configured as a multi-layer surface relief structure with one or more coating layers, a multi-layer embedded structure, or a multi-layer embedded structure with one or more coating layers. At least one of the materials of IRG 2105 may have at least one optical property that is different from the medium surrounding IRG 2105. For embedded structures, this medium is the substrate 2103, and for surface relief structures, this medium is the medium surrounding the substrate 2103, which may be air.

Alternatively, IRG 2105 may consist of a change in optical properties within a layer of thin material on the surface of substrate 2103 or within a layer of thin material within substrate 2103. In this case, the layer of material may be a liquid crystal, an optical polymer, or another material capable of supporting spatial changes in optical properties such as refractive index, electrical permittivity, permeability, birefringence and/or absorptivity.

In general, the structure and composition of IRG 2105 is preferably tailored so that the efficiency of the diffraction order results in a good balance of performance according to the characteristics listed in Table 3 of FIG. 71. As mentioned earlier, in order to have diffraction efficiency where the two-eye orders are non-zero, some form of symmetry breaking must exist under the condition of a perfectly symmetric interleaved grating.

Use of multiple diffractive waveguide couplers

The finite range of the xy-wavevector provided by the cropped waveguide region described by inequality (185) limits the range of combined wavelengths and fields of view that can be supported by a single DWC 2101. A composite DWC can be implemented by stacking two or more DWCs on top of each other. In principle, the wavelength range of projected light and/or the size of the field of view that can be displayed by such a system can be larger than that of systems relying on a single DWC. Projection light coupled out from a DWC further from the viewer's eye than the nearest DWC will pass through the DWC closer to the eye in the same way as in the real world. Therefore, the overall output of a composite DWC is a combination of the outputs of the individual DWCs. In such a system, each DWC only needs to process a portion of the wavelengths and/or viewing angles of the projection light required by the overall system. As long as the ranges of wavelengths and viewing angles handled by each DWC overlap to some extent, the total range of wavelengths of projected light and/or viewing fields of view that can be displayed by a composite DWC is based on a single waveguide composed of the same substrate material. It may increase compared to the wavelength and/or range of observation field of view of the DWC.

One way to achieve this is to use different grid periods p _x and p _y for the individual DWCs of the composite DWC. Based on inequality (185), each DWC may carry a different range of wavelengths and/or viewing angles of the projection light.

FIG. 22A shows, for example, a system where three DWCs 2201, 2202, 2203 are provided as part of an augmented reality display system. Each DWC (2201, 2202, 2203) is configured in a similar manner to DWC (2101). Additionally, a cover glass 2204 is integrated to protect the front surface of the DWC 2203. The DWC 2201 includes an input grating 2206 and an IRG 2208 configured as an output element of the DWC 2201, and is made of a substrate 2205 forming a planar slab waveguide. DWC 2202 is comprised of a substrate 2208 forming a planar slab waveguide incorporating an input grating 2209 and an IRG 2210 configured as the output element of DWC 2022. DWC 2203 is comprised of a substrate 2211 forming a planar slab waveguide into which an input grating 2212 and an IRG 2213 consisting of output elements of DWC 2203 are integrated. Preferably, the DWCs 2201, 2202, 2203 are parallel to each other to a high degree. A projector (not shown) generates an image bearing ensemble of light beams directed to the input grating 2206. While ensuring that the input gratings 2209, 2212 are positioned along the path of the projected light carried by the zero-order transmission of the preceding input grating, a non-negligible portion of the light incident on the input gratings 2206, 2209 is disposed along the path of the projected light transmitted by the zero-order transmission of the preceding input grating. By allowing it to be transmitted through them, the projected light can be coupled to all three DWCs. First, IRGs 2207, 2210, and 2213 overlap each other when viewed in the xy-plane, so that the output of each IRG can overlap, allowing observer 2214 to observe light from all three DWCs simultaneously. This allows you to view the combined image from the overlap of the DWC's output.

Projection light coupled to each DWC (2201, 2202, 2203) will operate in a similar manner as a single DWC (2101). In this case, each DWC has a grating period selected to suit the wavelength of the projection light output by the projector and/or a portion of the viewing field of view.

For a typical RGB color display, each waveguide can be optimized for single component colors: red, green, and blue. This optimization can be applied not only to the selection of the lattice periods p _x and p _y , but also to the structural design of the IRGs (2207, 2210, 2213). Using a smaller range of wavelengths can improve control of the diffraction efficiency because the intrinsic variation associated with the wavelength of the incident light beam can be significantly reduced. In this way, not only can an expanded viewing field of view and/or wavelength range be accommodated by the display system, but the performance of the system can be further optimized.

In another variation, multiple projectors may be used. Here, the output of each projector can be coupled to all DWCs in the stack or to some of the DWCs in the stack. FIG. 22B shows a top view of a DWC stack 2215 of three DWCs 2216, 2217, and 2218. DWC 2216 has an input grid 2219 and an IRG 2220 configured as an output element of the DWC. DWC 2217 has an input grid 2221 and an IRG 2222 configured as an output element of the DWC. DWC 2218 has an input grid 2223 and an IRG 2224 consisting of output elements of the DWC. The sizes and positions of the input grids 2219, 2221, and 2223 do not need to be the same when viewed in the xy-plane. Likewise, the size and position of IRGs 2220, 2222, and 2224 do not need to be the same when viewed in the xy-plane. In this configuration, separate projectors may be used to direct the projected light to each DWC 2216, 2217, and 2218. This may allow for an increase in field of view by facilitating the use of projectors with smaller field of view outputs by combining them with separate DWCs optimized for a portion of the total field of view of the system.

FIG. 22C shows a top view of another variation of the system using multiple DWCs 2225. In this system, three DWCs (2226, 2227, 2228) are placed adjacent to each other to provide an increase in the viewing field of view of the system in the xy-plane and/or an increase in the size of the system's eyebox in the xy-direction. DWC 2226 has an input grid 2229 and an IRG 2230 comprised of the DWC's output elements. DWC 2227 has an input grid 2231 and an IRG 2232 consisting of output elements of the DWC. DWC 2228 has an input grid 2233 and an IRG 2234 comprised of the DWC's output elements. Separate projectors may be used to send projected light to each DWC (2226, 2227, 2228). Preferably, in some configurations DWCs 2226, 2227 are joined together to form seam 2235 and DWCs 2227, 2228 are joined together to form seam 2236. In this configuration, it may be advantageous for the seam to include light absorbing material so that light from one DWC does not couple to the other. Each DWC 2226, 2227, 2228 may have its own design and may be optimized for a different range of wavelengths and viewing fields of projected light. In other configurations, DWCs 2226, 2227, 2228 do not need to be coplanar, and in some configurations it may be advantageous to turn DWCs 2226, 2227 inward toward the observer to create a wrap effect. This approach can further help increase the total field of view of the system.

It will be appreciated that in principle any number of DWCs may be used in a multiple DWC system, and that combinations of the methods described herein may be used. For example, one configuration could use several multiple stacked waveguides as shown in Figure 22A and placed adjacent to each other in a similar manner as shown in Figure 22C.

Fabrication process of interleaved rectangular grids

Practical use of DWCs featuring IRGs in output devices may require the use of fabrication processes that can create sub-micron scale optical structures or patterns of variation in optical properties. Depending on the intended application, these processes may need to be scaled up on a large scale and/or at low cost. Well-established processes suitable for use in IRG production include:

i) Ruling/scribing - a 1D grid can be created by precisely running a very sharp tool on a suitable substrate, and a second pass at a 90° transition can be performed to create a 2D rectangular grid; , which can be transferred to other materials through replication methods such as casting or embossing. However, the shapes that can be created with this method are very limited, and when applied to DWC, it is difficult to achieve as carefully controlled symmetry breaking as is required for many IRGs.

ii) Direct writing - using nanoscale fabrication processes such as focused ion beam milling (FIB) combined with computer control systems, a wide range of nanoscale structures, such as those required for IRGs using surface relief structures, can be directly printed. can do. Depending on the material for the DWC's substrate, this milling may go directly into the substrate, or it may be a thin layer of suitable material deposited on the substrate.

iii) lithography - using a method to create nanoscale patterns in a suitable resist material, followed by an etching process to remove material from the target area, a wide range of nanoscale structures suitable for IRG using surface relief structures can be created. You can. This process is very suitable for creating binary structures. These processes can be applied multiple times to create so-called multi-level structures with more complex shapes than binary structures. Patterning of the resist can be accomplished using direct printing of a single exposure point, such as e-beam lithography, or by a number of processes relying on replication of a base mask, which can be accomplished using conventional optical techniques, including UV/EUV lithography. It may be an enlarged version of the intended design, such as a lithography process. Depending on the material used for the substrate of the DWC, this lithography can be used to etch directly into the substrate or to etch a thin layer of a suitable material deposited on the substrate. Lithographic methods of coating a substrate with a multilayer material and then etching the layers using an appropriate resist material can provide IRGs of multilayer structures featuring various materials depending on the distance in the direction perpendicular to the plane of the grating.

iv) Replication to substrate - Methods such as direct printing or lithography can be used to form a mastering surface from which the IRG can be replicated to the substrate. The molding method herein, such as nano-imprint lithography, inverts the master pattern in moldable materials such as thermoplastic resin, UV-curable resin, and thermally-curable resin. Can be used to clone an (inverse) version. These resins can be applied as a thin coating layer on a substrate, followed by a patterning step with a mastering surface and a curing step to define the structure. Replication allows for increased volume and cost savings for DWC parts compared to direct printing and lithography methods. After mastering, multiple replication steps can be applied to increase the number of available molds or to provide a mold with multiple dies of the same size. The replication method can be applied to rigid substrates such as glass wafers (cover wafers) or flexible substrates such as polymer films. Flexible substrates can be used in a reel-to-reel method for application of nano-imprinted structures. The resulting nano-imprinted foil can be applied to a rigid substrate in a separate lamination process.

v) Injection molding/casting - methods such as direct printing or lithography can be used to form the mastering tool. When properly configured, this mastering tool can be integrated into an injection molding tool and used to fabricate substrate components from thermoplastics, where the IRG is formed as a surface relief structure that is an integral part of the molded substrate. Thermosets can also be formed into similar parts using related casting processes.

vi) Patterning liquid crystals - pattern exposure methods can be used to generate IRGs realized by periodic changes in liquid crystal orientation, inducing orientation in thin layers of liquid crystal polymers which can then be cured with a set resin (e.g. using UV light-polymerization) ). Thereafter, multiple layers can be formed with changes in liquid crystal orientation in each layer allowing the formation of a three-dimensional structure of oriented liquid crystal. Here, the patterning of the orientation of the liquid crystal will follow the principle of an interleaved rectangular grid with the grid plane being parallel to the liquid crystal layers. Orientation of liquid crystals prior to in situ curing can be achieved by a direct printing method using a tightly focused UV laser. It is very difficult to achieve sufficient resolution to enable the fabrication of IRGs using these methods.

0.035)로 인해 일반적으로 무시할 수 없는 회절 효율을 생성하기 위해서는 여러 레이어들이 필요할 것이다. 그러나, 레이어의 수가 너무 많아서, 3차원 브래그 효과가 크게 나타나서는 안 된다.vii) Photopolymer exposure - Another approach to generate IRGs realized by changes in optical properties embedded in layers of materials is the use of specific photopolymers. Materials such as Bayfol® HX film (Covestro AG) can be modified by exposure to intense light so that the refractive index of the film changes. This modification can be achieved by interfering different light beams, or by using focused light beams in a direct printing method. In both cases, it is very difficult to form structures small enough to be used to make IRGs with visible light. Additionally, the small refractive index differences provided by these materials (e.g. Δn in Bayfol® HX film

0.035), multiple layers will typically be required to produce a non-negligible diffraction efficiency. However, because the number of layers is too large, the 3D Bragg effect should not appear significantly.

viii) Coating - As discussed elsewhere, coating processes can be used to add one or more layers of different materials that can modify the optical properties of the IRG. These processes can be applied in a directional manner, such as well-collimated physical vapor deposition, or in a less directional selective manner, such as an oriented tumbling process using PVD, a plasma coating process, or a conformal coating atomic layer deposition.

ix) Encapsulation/lamination/multilayering - IRG manufactured with a surface relief structure can be made into a structure that is basically encapsulated and embedded in a material that extends the substrate to surround the IRG. Over-molding offers a range of methods for this. Another approach may use a thin adhesive layer sufficient to encapsulate the surface relief structure, laminated with a second layer of substrate material, which may or may not be the same material as the original substrate. Related methods can also be used to create multilayer structures. Here, a resin coating process of a material different from the previously formed surface relief structure is undertaken to encapsulate the structure and provide a new base layer from which additional surface relief structures can be formed. As mentioned elsewhere, by carefully controlling the thickness of these layers, it is possible to exploit consistent effects between the layers, allowing a greater degree of control over the diffraction scattering properties of IRGs formed by this approach.

Additional examples of interleaved rectangular gratings used in diffractive waveguide couplers

The general layout shown in Figures 21A and 21B is suitable to accommodate a wide range of examples of the present invention, but the shape of the overall DWC, the precise location and shape of the different grating areas and other optical elements, as well as the design position of the grating relative to the observer, may vary. It will be appreciated by those skilled in the art that specific details, such as selection of period, will depend on the specific design needs of the system, such as intended projector viewing field of view, eyebox size, wearing position, and design form factor.

Many specific embodiments of the invention now follow. These cases are illustrative, and it will be understood by those skilled in the art that there are many, many designs made possible by the present invention and methods disclosed herein.

Example 1: Interleaved rectangular grids using scaling to introduce shape symmetry breaking

23 is a top view of a unit cell 2301 that can be repeated across the xy-plane to form IRG 2302. IRG (2302) may be configured to be used as an output element of a DWC such as DWC (2101). IRG 2302 has a surface relief structure that protrudes into the surrounding medium, in this case the air. The periodic structure PS1 of IRG 2302 has a rectangular cross-sectional shape when viewed in the plane of the grid and is composed of a copy of structure S1 2320 that protrudes from the plane of the grid into the surrounding air. Structure S1 (2303) has side lengths of S1 _x and S1 _y in the x- and y-directions, respectively. In this example, S1 _y >S1 _x . The period of the lattice L1 and L2 of the IRG 3502, that is, the length of the sides of the unit cell 3501, is p _x in the x-direction and p _y in the y-direction.

The periodic structure PS2 of IRg 2302 also consists of a copy of structure S2 2304, which has a rectangular cross-section when viewed in the plane of the grid and protrudes out of the plane of the grid into the surrounding air. Structure S2 2304 has side lengths S2 _x and S2 _y in the x-direction and y-direction, respectively. Due to the selected position of unit cell 2301, there are four separate copies of structure S2 2304 within unit cell 2301. Structures S1 (2303) and S2 (2304) have the same material composition and materials as each other.

In the example shown in Figure 23, and You can check. By changing the size and/or shape of structure S1 (2303) and/or structure S2 (2304), the efficiency of the diffraction order can be varied.

Figures 24, 25, and 26 show various graphs for calculating the diffraction efficiency of IRGs formed from a specific example of the unit cell shown. For these _calculations , _p Unless otherwise stated, the incident beam used in the calculations has a vacuum wavelength of 528 nm and is incident at a spherical angle by equation (7) with θ = 55° and ϕ = 90°.

Figure 24 shows a series of graphs showing how the diffraction efficiency of the conversion orders and two-eye orders varies based on the degree of shape difference between one optical structure array relative to another optical structure array.

Insets 2401, 2402, and 2403 illustrate example unit cells that may constitute IRG 2105 as previously described. The x-axis and y-axis of this graph are normalized to the period p _x in the x-direction and the period p _y in the y-direction of the IRG, respectively. The structures shown at 2401, 2402, 2403dp have the same parameters as IRG 2302, and in all cases the structure S1 in the insets has rectangular side lengths given by S1 _x =0.4p _x and S1 _y =0.4p _y .

The structure S2 in the insets 2401, 2402, and 2403 has the same length parameter in the y-direction given by S2 _y =0.4p _y . Structure S2 in inset 2401 has a length parameter of 0 in the x-direction, which essentially means that there is no structure S2 in this unit cell. In inset 2402, structure S2 has _a length parameter _S2 This means it will be a rectangular grid (FSIRG). Structure S2 in inset 2403 has a length parameter S2 _x =0.8p _x in the x-direction. Accordingly, the insets 2401, 2402, 2403 show a trend in size in the x-direction from none to identical to structure S1 to much longer than structure S1.

Graphs 2404 and 2405 show the results of calculations of diffraction efficiency for various diffraction orders of IRG 2101 constructed from the general case of structures S1 and S2 shown at 2041, 2402 and 2403dp. In this graph, the size of structure S2 in the x-direction depends on the parameter s _x such that S2 _x =s _x p _x . Graph 2404 shows how the diffraction efficiency of {-1,-1} TX and {1, -1} T+ _X transition orders varies with s ,-1} Shows how the diffraction efficiency of the STE two-eye order changes with respect to s _x .

Points 2406, 2407 correspond to the unit cell shown at 2401, which is essentially a rectangular grid in which the transition orders have relatively low efficiency, while the two-eye orders have relatively high efficiency. shows that Points 2408 and 2409 correspond to the unit cell shown at 2402, where the conversion order shows moderate efficiency, while the two-eye order shows zero efficiency, as expected. Points 2410 and 2411 correspond to the unit cell shown at 2403, which is the general case of IRG, showing that the diffraction efficiencies of both transition orders and two-eye orders are relatively high. In the region between s _x =0.4 and _s It shows how much control can be had.

Figure ₂₅ shows _the transition orders and _to- It shows a series of graphs showing how the diffraction efficiency changes for eye orders. Here, the parameter s _y is used to define the length of the structure S2 in the y-direction, such that S2 _y = s _y p _y . The inset 2502 shows a case where s _y = 0.4 and the unit cell is the same as the inset 2502. The inset 2502 shows a case where s _y = 0.4 and the unit cell is the same as the inset 2502. The inset (2503) shows the case where s _y =0.8.

Graphs 2504 and 2505 show calculation results of diffraction efficiency for various diffraction orders of IRG 2101 composed of structures S1 and S2 of the type shown in insets 2501, 2502, and 2503. Here, the length of structure S2 in the y-direction depends on the parameter s _y . Points 2506 and 2507 correspond to the unit cell shown at 2503. The behavior of diffraction efficiency is similar to that shown in graphs 2404 and 2405. However, while the TX, T+X transition order diffraction efficiency of point 2506 is similar to that of point 2410, the STE to-eye order diffraction efficiency of point 2508 is significantly lower than that of point 2411. Nonetheless, significant variation is still seen in the STE to-eye order between the values s _y =0.4 and s _y =0.8. Therefore, the relative size of S2 to structure S1 not only affects the strength of the two-eye order, but can also greatly affect the horizontal vs. aspect ratio of the shape of structure S2.

Figure 26 shows a series of heatmaps showing the change in diffraction efficiency of various diffraction orders for the x- and y-direction dimensions of structure S2 of IRG 2302. Here the rectangular structure S1 _is fixed with _the dimensions S1 _x =0.4p _x and S1 _y = _{0.4p y} , while _the rectangular structure S2 has the _{numbers S2} Heatmap 2601 shows the change in diffraction efficiency of {0,-1} STE two-eye order upon reflection. It can be seen that the diffraction efficiency is approximately greatest when D _x =D _y =0. Heatmap 2602 shows the change in diffraction efficiency of {1,-1} T+X transition order upon reflection. It can be seen that the diffraction efficiency is approximately greatest when D _x =D _y =0. Heatmap 2603 shows the change in diffraction efficiency of {-1,0} TEAT+X two-eye order upon reflection. It can be seen that the diffraction efficiency is approximately greatest when D _x =D _y =0. The heatmap (and 2604) is the {0,-1} STE two-eye order over the product of the diffraction efficiency of {1,-1} T+X conversion order and {-1,0} TEAT+X two-eye order. It shows the ratio of diffraction efficiency. For some configurations of DWC, it has been found that there is a benefit in uniformity of output if this ratio is close to unity. As shown in heatmap 2604, this identifies the region near s _x =0.5 and s _y =0.8.

Example 2 - Interleaved rectangular grids using relative lattice position shift to introduce position symmetry breaking.

FIG. 27 shows a top view of a unit cell 2710 that can be repeated across the xy-plane to form IRG 2702. IRG (2702) may be configured for use as an output element of a DWC, such as DWC (2101). IRG 2702 may have a surface relief structure that protrudes into the surrounding medium, in this case the air.

Structures S1 (2703) and S2 (2704) of IRG (2702) have the same size, shape, and material composition. The structure has a circular cross-section when viewed in the plane of the grid, and protrudes out of the plane of the grid towards the surrounding air. The period of the lattice L1 and L2 of the IRG 2702 and the length of the side of the unit cell 2701 are thus p _x in the x-direction and p _y in the y-direction. The lattice offset vector of IRG 2702 has a value defined as (195).

(195)

Likewise, D _x and D _y are lattice shift parameters to describe the displacement between the lattice L1 and L2 of IRG 2702. It should _be noted that when _{D Accordingly} , the parameters _D In some arrangements, the shift can be made only in the x-direction or y-direction by setting D _y =0 or D _x =0, respectively.

28A-28C, 29A-29C, 30, 31 and 32 show various graphs for calculation of the diffraction efficiency of IRGs formed from specific examples of the unit cells shown. For these _calculations , _p Unless otherwise stated, the incident beam used in the calculations has a vacuum wavelength of 528 nm and is incident at a spherical angle by equation (7) with θ = 55° and ϕ = 90°.

28A-28C show two diffraction orders for angle of incidence θ resulting in various shifts between lattice L1 and L2 of IRG 2702. Here the circular structures S1 and S2 of IRG have a diameter of 0.4p _x . Figure 28A shows unit cell 2801. In this unit cell 2801, lattice L1 of IRG 2702 is shifted in the positive x-direction with respect to lattice L2 (i.e., D _x >0 and D _y =0). The graph 2802 in FIG. 28A shows, for this arrangement, the reflection for the angle of incidence on the IRG 2702 of a light beam with the xy-wavevector pointing only in the y-direction: {-1,-1} TX and {1, -1} Shows the change in diffraction efficiency of T+X transition orders. As shown in graph 2802, the diffraction efficiency of the T+X conversion orders is the same as the TX conversion order.

Figure 28B shows unit cell 2803. In unit cell 2803, the lattice L1 of the IRG is shifted in the positive x-direction and negative y-direction with respect to the lattice L2 (i.e., D _x >0 and D _y <0). Graph 2804 in FIG. 28B shows, for this arrangement, the {-1,-1} TX and {1, -1} Shows the change in diffraction efficiency of T+X transition orders. As shown in graph 2804, the diffraction efficiency of the TX transition order is different from the T+X transition order in this arrangement, with the TX order being relatively stronger.

Figure 28C shows unit cell 2804. In unit cell 2805, lattice L1 is shifted relative to lattice L2 in the positive x-direction and positive y-direction (i.e., D _x >0 and D _y >0). The graph 2806 in FIG. 28C shows, for this arrangement, the angle of incidence on the IRG 2702 of a light beam with an xy-wavevector pointing only in the positive y-direction, with {-1,-1} TX and {1, -1} Shows the change in diffraction efficiency of T+X transition orders. As shown in graph 2806, the diffraction efficiency of the TX transition order is different from the T+X transition order in this arrangement, with the T+X order being relatively stronger.

Accordingly, a difference in the transition orders produced by having a displacement from the center position in both the x-direction and the y-direction can be achieved. By changing the shift, the diffraction efficiency of the transition orders can be emphasized to some extent.

Figures 29a-29c show that the same effect as described with respect to Figures 28a-28c can also be achieved for square nanostructures. here am.

Figure 29A shows unit cell 2901. In unit cell 2901, lattice L1 is shifted in the positive x-direction with respect to lattice L2 (i.e., D _x >0 and D _y =0). Graph 2902 in FIG. 29A shows the diffraction of the {-1,-1} TX and {1,-1} T+X transition orders versus the angle of incidence of the light beam on the IRG with unit cell 2901 for this arrangement. Shows the change in efficiency, where the xy-wavevector of the incident beam points only in the positive y-direction. As shown in graph 2902, the diffraction efficiencies of the T+X and TX transition orders are the same for this arrangement.

Figure 29B shows unit cell 2903. In unit cell 2903, lattice L1 is shifted in the positive x-direction and negative y-direction relative to lattice L2 (i.e., D _x >0 and D _y <0). Graph 2904 in FIG. 29B shows the diffraction of the {-1,-1} TX and {1,-1} T+X transition orders versus the angle of incidence of the light beam on the IRG with unit cell 2903 for this arrangement. Shows the change in efficiency, where the xy-wavevector of the incident beam points only in the positive y-direction. As shown in graph 2904, the diffraction efficiency of the TX transition order in this arrangement is different from the T+X transition order, with the TX order being relatively much stronger.

Figure 29C shows unit cell 2905. In unit cell 2805, lattice L1 is shifted relative to lattice L2 in the positive x-direction and positive y-direction (i.e., D _x >0 and D _y <0). The graph 2906 in FIG. 29C shows the diffraction of the {-1,-1} TX and {1,-1} T+X transition orders versus the angle of incidence of the light beam on the IRG with unit cell 2905 for this arrangement. Shows the change in efficiency, where the xy-wavevector of the incident beam points only in the positive y-direction. As shown in graph 2906, the diffraction efficiency of the TX transition order in this arrangement is different from the T+X transition order, with the T+X order being relatively much stronger.

30 shows how changing the shift between lattices L1 and L2 of IRG 2702 in the y-direction affects the T-X and T+X transition orders in reflection and the diffraction efficiencies of STE to-eye order in reflection. shows.

Unit cell 3001 is a specific example of IRG 2702 with lattice displacement parameters given by D _x =0.25, D _y =0. Unit cell 3002 is a specific example of IRG 2702, which is a FSIRG and has a lattice displacement parameter given by D _x =D _y =0. Unit cell 3003 is another example of IRG 2702 with lattice displacement parameters given by D _x =0 and D _y =-0.25.

Graph 3004 shows how the diffraction efficiency of the transition orders of TX and T+X varies with the parameter D _y of IRG 2702. Graph 3005 shows how the diffraction efficiency of STE two-eye order varies with the parameter D _y of IRG 2702. Points 3006, 3007 correspond to unit cell 3002 and show that, as expected, the diffraction efficiency of the STE two-eye order is zero, and the diffraction efficiency of the TX and T+X transition orders is maximum for D _y . Point 3008 corresponds to unit cell 3001 and point 3009 corresponds to unit cell 3003. Both points 3008 and 3009 show a significant decrease in diffraction efficiency compared to point showing that changing D _y has a modest effect on the relative efficiency of the TX and T+X conversion orders. Point 3010 corresponds to unit cell 3001 and point 3011 corresponds to unit cell 3003. Both points 3010 and 3011 show a significant increase in the diffraction efficiency of the STE two-eye order as a result of the change in D _y . Therefore, in the case of IRG 2702, shifting lattice L1 with respect to lattice L2 in the y-direction can introduce two-eye order in a controlled manner. As can be seen in these figures, changing the lattice offset parameters can control the diffraction efficiency of the diffraction orders produced by IRG 2702.

Points 3008 and 3009 have the same value as points 3010 and 3011. This is because the IRG generated in the unit cell 3001 is the same as the IRG generated in the unit cell 3003. This can be seen by identifying that shifting the position of the reference rectangle for unit cell 3101 by 0.75p _x in the x-direction and 0.5p _y in the y-direction results in unit cell 3103.

Figure 31 shows how changing the shift between the lattice L1 and L2 of IRG 2702 in the x-direction affects the diffraction efficiency of the diffraction orders of T-X and T+X and the STE to-eye order.

Unit cell 3101 is a specific example of IRG 2702 with lattice displacement parameters given by D _x =0.25, D _y =0. Unit cell 3102 is another example of IRG 2702, where D _x = D _y = 0 and is a FSIRG. Unit cell 3103 is a further example of IRG 2702 with lattice displacement parameters given by D _x =-0.25, D _y =0.

Graph 3104 shows how the diffraction efficiency of the TX and T+X transition orders varies with the parameter D _x of the IRG 2702. Graph 3105 shows how the efficiency of the STE two-eye order varies with the parameter D _x of the IRG 2702. Points 3106, 3107 correspond to unit cell 3102 and show that, as expected, the diffraction efficiency of the STE two-eye order is zero, and the diffraction efficiency of the TX and T+X transition orders is maximum for D _x . Point 3108 corresponds to unit cell 3101 and point 3109 corresponds to unit cell 3103. Both points show a significant decrease in diffraction efficiency compared to the point showing that changing D _y has a modest effect on the relative efficiency of the TX and T+X conversion orders. Point 3110 corresponds to unit cell 3101 and point 3111 corresponds to unit cell 3103. Both points show a significant increase in diffraction efficiency of the STE two-eye order as a result of changing D _x . Accordingly, by shifting lattice L1 in the x-direction with respect to lattice L2 in the case of IRG 2702, two-eye orders can be introduced. As can be seen in these figures, changing the lattice offset parameters can control the diffraction efficiency of the diffraction orders produced by IRG 2702.

Points 3108 and 3109 have the same values as points 3110 and 3111. This is because the IRG generated in the unit cell 3101 is the same as the IRG generated in the unit cell 3103. This can be seen by identifying that shifting the position of the reference rectangle for unit cell 3101 by 0.75p _x in the x-direction and 0.5p _y in the y-direction results in unit cell 3103.

Figure 32 shows a series of heatmaps showing the change in diffraction efficiency of various diffraction orders with respect to the relative lattice shift parameters D _x and D _y of IRG 2702. Heatmap 3201 shows the change in diffraction efficiency of {0,-1}STE two-eye order. The diffraction efficiency is approximately and The biggest thing can be known when Heatmap 3202 shows the change in diffraction efficiency for {1,-1} T+X transition order. The diffraction efficiency is approximately The biggest thing can be known when Heatmap 3203 shows the change in diffraction efficiency of {-1,0} TEAT+X two-eye order. The diffraction efficiency is approximately and The biggest thing can be known when Heatmap 3204 is the product of the diffraction efficiency of {1,-1} T+X conversion order and {-1,0} TEAT+X two-eye order of the {0,-1} STE two-eye order. Shows the ratio of diffraction efficiency. For some configurations of DWC, it has been found that there is an advantage in uniformity of output if this ratio is neither too large nor too small and is close to unity. As shown at 3204, this Identify the area around the phosphorus.

33A-33D and 34A-34D provide a series of heatmaps showing ray tracing simulation results of the luminance output that would be observed when DWC 2101 is configured as a variant of IRG 2702 as output element 2105. . The heatmap shows the predicted luminance output from the IRG in terms of horizontal and vertical angles, where the input has uniform luminance over the viewing angle across the rectangular field of view. For the purposes of this simulation, =528 nm, p_x=p_y=355 nm, the height of the structure is 100 nm, the IRG is made of a material with a refractive index of 1.82 and is on a substrate with a refractive index of 1.82.

Figures 33A-33D show observable results of how the displacement of lattice L1 relative to lattice L2 of IRG 2702 affects the generated two-eye orders. Each of the different unit cells 3301 to 3304 has its respective ray tracing heatmap displayed in the insets 3305 to 3308.

Figure 33A shows a unit cell 3301 and its heatmap 3305. Unit cell 3301 is Corresponds to the in lattice shift parameter, i.e. FSIRG. As can be seen in the corresponding ray tracing heatmap 3305, the output is zero as a result of the diffraction efficiency of the two-eye orders being zero.

Figure 33B shows a unit cell 3302 and its heatmap 3306. Unit cell 3304 is and Corresponds to the in lattice shift parameter. As can be seen in the corresponding ray tracing heatmap 3306, non-zero luminance is achieved as a result of the diffraction efficiency of the two-eye orders being zero.

Figure 33C shows a unit cell 3303 and its heatmap 3307. Unit cell 3304 is and Corresponds to the in lattice shift parameter. As can be seen in the corresponding ray tracing heatmap 3307, the diffraction efficiency of the two-eye orders is non-zero, and as a result of the increase in diffraction efficiency of these orders due to increase in D _y , the heatmap 3306 A relatively increased level of luminance can be confirmed.

Figure 33D shows a unit cell 3304 and its heatmap 3308. Unit cell 3304 is and Corresponds to the in lattice shift parameter. As can be seen in the corresponding ray tracing heatmap 3308, the diffraction efficiency of the two-eye orders is non-zero, and as a result of the further increase in the diffraction efficiency of these orders due to a further increase in D _y , the heatmap A relatively increased level of luminance can be confirmed for (3307).

Accordingly, increasing the y-direction displacement of lattice L1 relative to lattice L2 of IRG 2702 can increase the resulting two-eye orders. However, from heatmaps 3306 to 3308, it is also clear that the luminance has low uniformity across viewing angles, resulting in a bright central band and low luminance elsewhere. Since the input luminance used in the simulation was uniform, this is a result of the interaction between the various beam paths through the DWC 2101 resulting from different orders of diffraction efficiency.

Figures 34A-34D provide a series of heatmaps showing ray tracing simulation results of the luminance output that would be observed if DWC 2101 was configured as a variant of IRG 2702 as the output element 2105. The heatmap shows the expected luminance for horizontal and vertical viewing angles, i.e., viewing directions projected into the xy-plane and yz-plane, respectively. Figures 34A-34D show observable results of how the displacement of lattice L1 relative to lattice L2 of IRG 2702 affects the generated two-eye orders. For each different unit cell 3401-3040, respective ray tracing heatmaps are shown in insets 3405-3408.

Figure 34A shows a unit cell 3401 and its heatmap 3405. Unit cell 3301 is Corresponds to the in lattice shift parameter, i.e. FSIRG. As can be seen in the corresponding ray tracing heatmap 3405, the output is zero as a result of the diffraction efficiency of the two-eye orders being zero.

Figure 34B shows a unit cell 3402 and its heatmap 3406. Unit cell 3402 is and Corresponds to the in lattice shift parameter. As can be seen in the corresponding ray tracing heatmap 3406, non-zero luminance is achieved as a result of the diffraction efficiency of the two-eye orders being zero.

Figure 34C shows a unit cell 3403 and its heatmap 3407. Unit cell 3403 is and Corresponds to the in lattice shift parameter. As can be seen in the corresponding ray tracing heatmap 3407, the diffraction efficiency of the two-eye orders is non-zero; As a result of the increased diffraction efficiency of these orders due to the increase in , a relatively increased level of luminance can be seen for the heat map 3406.

Figure 34D shows unit cell 3404 and its heatmap 3408. Unit cell 3304 is and Corresponds to the in lattice shift parameter. As can be seen in the corresponding ray tracing heatmap 3408, the diffraction efficiency of the two-eye orders is non-zero, and as a result of the further increase in the diffraction efficiency of these orders due to the further increase in D_x, the heatmap ( 3407), a relatively increased level of luminance can be confirmed.

Accordingly, increasing the x-direction displacement of lattice L1 relative to lattice L2 of IRG 2702 can increase the resulting two-eye orders. However, from the heatmaps 3406 to 3408, it is clear that the luminance uniformity is much better compared to 3306 to 3308. In all cases, the input luminance used in the simulations was uniform, so the difference here is that different diffraction orders create a more favorable balance between the various beam paths through DWC 2101, resulting in a more uniform luminance output. shows that

The drawings and embodiments described above introduce a degree of breaking the symmetry of the interleaved rectangular lattice, such as by modifying the form of either the structure S1 or S2 of the IRG, or the lattice offset vector o _xy of the IRG, and then output these IRGs. It is possible to achieve customization of the degree of efficiency of the resulting diffraction order, which can be used to advantageously manipulate the uniformity of luminance output from the DWC used as the device.

Example 3 - Interleaved rectangular grids using general shape modification to introduce shape symmetry breaking.

Figure 35A shows a top view of a unit cell 3501 that can be repeated across the xy-plane to form IRG 3502. The IRG (3502), like the DWC (2101), can be configured to be used as an output element of the DWC. IRG 1902 has a surface relief structure that protrudes into the surrounding medium, in this case air. Structures S1 and S2 of IRG 3502 are defined to have identical optical properties. The period of the lattice L1 and L2 of the IRG 3502, that is, the length of the sides of the unit cell 3501, is p _x in the x-direction and p _y in the y-direction. The offset vector o _xy of IRG (3502) is It has the value of

Structure S1 of IRG (1902) is a pillar (3503) whose cross-sectional shape is circular when viewed from the lattice plane. Structure S1 is It has a radius of Structure S2 is represented by a plurality of elements 3504, 3050 within the unit cell, and is a slab of material that is uniform throughout the unit cell such that the two elements 3504, 3505 remain positioned in the lattice plane with structure S1. It is formed by cutting an oval-shaped cross section from. The ellipse is centered on the unit cell 3501, and the parameters and It has a size described by . Structure S1 is defined to be smaller than the ellipse defining structure S2. if, Then, the major axis of the ellipse is in the y-direction It has a size of , and the minor axis of the ellipse is in the x-direction. has the size of in this case am. if, Then, the major axis of the ellipse is in the y-direction It has a size of , and the minor axis of the ellipse is in the x-direction. has the size of in this case am. If the If so, the oval is circular and am.

As a result of the structure S2 of IRG 3502 extending to the edge of the unit cell 3501, the structure of the periodic structure PS2 of IRG 3502 will be continuous when the structure is tilted across the plane by r _x <0.5. Figure 35B shows a 3x3 array of copies of unit cell 3501 showing how structure S2 joins together to form continuous structures in IRG 3502.

36 shows parameters describing the unit cell 3501. and A series of heat maps showing the change in diffraction efficiency for various diffraction orders are shown. For these _calculations , _p The incident beam used in the calculations has a wavelength of 528 nm in vacuum and is incident at a spherical angle according to equation (7) with θ = 55° and ϕ, as indicated in the title of each heatmap.

Example 4 - Interleaved rectangular grids using inversion modification of another interleaved rectangular grid

Figure 37 shows a perspective view of a portion of IRG 3701 formed from unit cell 3501. By applying an inversion modification to the unit cell, a new IRG structure 3702 can be formed. The structures S1 and S2 specified as a result of the modification are characterized by a lack of material, but they will still follow the same rules as for the periodic structures PS1 and PS2.

Figure 38 shows a series of heatmaps showing the change in diffraction efficiency of various diffraction orders with parameters r ₁ and ry describing a unit cell 3501 followed by inversion modification to form structure 3702. For these _calculations , _p The incident beam used in the calculations has a wavelength of 528 nm in vacuum and is incident at a spherical angle according to equation (7) with θ = 55° and ϕ, as indicated in the title of each heatmap.

Diffractive waveguide coupler with multiple grating elements.

In some embodiments, it is desirable to use multiple interleaved rectangular gratings within the diffractive waveguide coupler to bring additional degrees of freedom to optimize the performance of the DWC. FIG. 39A shows a perspective view of a DWC 3901 comprised of a planar substrate 3902 arranged such that the planes of the waveguide are parallel to the xy-plane of the Cartesian (x,y,z)-coordinate system. Figure 39b shows a cross-sectional view of the same DWC 3901.

Projector 3910 uses output projection light coupled to DWC 3901 by a series of input gratings 3903, 3904, 3905. When viewed in the xy-plane of DWC 3901, the input gratings 3903, 3904, and 3905 have the same dimensions, shape, and location as each other, but are separated in the z-direction. The input grating 3903 is located on the waveguide plane of the DWC 3901 closest to the projector 3910, the input grating 3904 is embedded midway between the waveguide planes of the DWC 3901, and the input grating 3905 is located on the waveguide plane of the DWC 3901 closest to the projector 3910. It is located on the waveguide of DWC (3901), which is furthest from (3910). The size and shape of the area covered by input gratings 3903, 3904, 3905 in the xy-plane is sufficient to receive a complete ensemble of light beams output by projector 3910.

Projection light coupled to the waveguide region in k-space propagates from the input grating to a series of output grating elements 3906, 3908, 3908 configured as IRGs. When viewed in the xy-plane of DWC 3901, IRGs 3906, 3907, and 3908 have identical dimensions, shapes, and positions, but are separated in the z-direction. IRG 3906 is located on the waveguide plane of DWC 3901 closest to the projector 3910, IRG 3907 is embedded midway between the waveguide planes of DWC 3901, and IRG 3908 is located on the waveguide plane of DWC 3901 closest to the projector 3910. It is located on the waveguide of the furthest DWC (3901). The size and shape of the area covered by IRGs 3906, 3907, 3908 in the xy-plane is , in the yz-plane Inequalities (193) and (194) based on the light projected to have a field of view of It matches.

Input grids 3903, 3904, and 3905 all have the same grid vector g ₁ as given by equation (182) and have periods p _y based on the same design principles as input grid 2104, so that inequalities (187) and ( 188) is satisfied. Likewise, IRGs 3906, 3907, ₃₉₀₈ all have the _same grid vectors _g With a period p _y based on the same design principle as IRG (2105), inequalities (191) and (192) are satisfied. Preferably, the IRGs are separated by a distance along the z-direction that is greater than the coherence length of the projected light. In this situation, the interaction of each output grating element and the light beam can be considered independent of the other elements, which simplifies the design and analysis of DWC 3901.

Each input grating 3903, 3904, 3905 provides the opportunity to couple the projected light to the waveguide region of k-space to be transmitted through the waveguide. The grid vectors of the input grid are the same, but the design and configuration of the unit cells do not need to be the same. As such, different gratings can be optimized to provide preferred properties, such as more optimal coupling through the transmission or reflection diffraction order, or more optimal coupling over a range of wavelengths. In general, the use of a plurality of input grating means allows each incident beam of projected light to produce input beams that are shifted relative to each other. This can advantageously provide coverage of the output eyebox.

Each IRG 3906, 3907, 3908 can provide cumulative orders listed in Table 1 of Figures 69 and diffraction orders listed in Table 2 of Figure 70. The geometry, composition and optical properties of the periodic structures that make up each IRG may be different. This provides the possibility that different IRGs can be optimized to have scattering properties that can result in favorable performance for the DWC 3901. In particular, gratings can be designed to have different magnitudes of diffraction efficiency for various diffraction orders and different dependences on the wavelength, direction, and polarization of the incident light beam.

For example, in some configurations, IRG 3906 may be configured as FSIRG and have only transition orders with non-zero diffraction efficiency, while IRG 3907 may be configured as HSIRG and IRG 3908 as VSIRG. It can be configured to provide a mix of two-eye and turn back orders. By separating the gratings, additional control may be possible to improve the performance of DWC 3901, especially as it relates to the characteristics listed in Table 3 of FIG. 71. The only two-eye orders of VSIRG for which the diffraction efficiency is non-zero are the TEAT+X and TEAT-X orders. These orders require that the waveguide beam of projected light first undergo a T+X or T-X transition order before output is possible. Likewise, the only two-eye orders of HSIRG for which the diffraction efficiency is non-zero are the STE and TEAT-Y orders.

Therefore, in the case of DWC 3901 where IRG 3906 is FSIRG, IRG 3907 is HSIRG, and IRG 3908 is VSIRG, IRG 3906 will be designed to provide transition orders for distributing the light beam throughout the grating. While the IRG 3908 provides the output of this light beam after switching, the IRG 3907 provides the output of this light beam by order T+X, T-X before switching or by TTB+X, TTB-X, UT+X or UT after switching. Provides the output of projected light by -X orders. The magnitude of the diffraction orders provided by each IRG can be controlled by modifying various properties, as discussed elsewhere in this description, but relative to the medium surrounding DWC 3901 and/or substrate 3902. It may include the height, size and shape of the structure made of materials with optical properties. In particular, the IRG 3907 embedded in the substrate 3902 must have optical characteristics that contrast with those of the surrounding substrate.

In some configurations, it may not be necessary to configure the output grating elements 3906, 3907, 3908 with an IRG. For example, if device 3908 were instead made with a 1D grating with a grating vector equal to _g Provides -I orders, but not other orders such as BT-Y and BRT+Y orders. Alternatively, element 3908 may be comprised of a rectangular grating (3908), which would provide the full range of diffraction orders listed in Table 2 of FIG. 70, without using symmetry-based modification of the diffraction efficiency of specific orders. You can.

In some configurations, only one or two of input grids 3903, 3904, and 3905 may be included in DWC 3901. Likewise, in some configurations, only one or two of output grids 3906, 3907, and 3908 may be included in DWC 3901. In other configurations, the number of input grids or output grid elements may be greater than three.

In some configurations, the output grating elements 3906, 3907, and 3908 are comprised of optical structures whose optical properties exhibit a strong dependence on the wavelength. In this arrangement, each grating element can be designed to exhibit significant variations in optical properties relative to the surrounding material over a small range of wavelengths, such that each grating element can be optimized for that range of wavelengths. In some configurations, the properties of grating elements 3906, 3907, 3908 and input gratings 3903, 3904, 3905 each provide only non-negligible diffraction efficiencies for non-zero diffraction orders in a small range of wavelengths. will be.

By matching the wavelength range of each input grating to the corresponding output grating, and ensuring that this wavelength range is distinct from the wavelength range of other input and output grating pairs, a beam of a given wavelength will only interact non-negligibly with the input and output grating pairs. It must be possible to ensure that this is done. For example, in some configurations input grating 3903 and output grating element 3906 can interact significantly with light in the 440 to 480 nm range, corresponding to blue light, and input grating 3904 and output grating element 3907 ) can significantly interact with light in the 520 to 560 nm range, corresponding to green light, and the input grating 3905 and output grating element 3908 can significantly interact only with light in the 600 to 640 nm range, corresponding to red light. there is.

If the wavelength ranges for the various grating pairs do not overlap, in some configurations the grating vectors for the input gratings 3903, 3904, and 3905 need not be identical to each other, and the grating vectors for the output grating elements 3906, 3907, and 3908 do not overlap. The grid vectors do not need to be identical to each other. In this case, the values of the grating period p _x and p _y can be optimized for the wavelength range of each grating pair. Advantageously, it may be desirable for each pair of input and output grids that one of the grid vectors of the output grid is the same as the grid vector of the input grid.

By reducing the range of wavelengths that must be accommodated by the input and output grating pairs, one can increase the size of the viewing field of view that can be accommodated within inequalities (187), (188), (191), and (192). Therefore, the observation field that can be accommodated by DWC can be increased. In a sense, such an approach is similar to using multiple DWCs, except that the wavelength-dependent properties of the grating rather than separate waveguides are used. If the grating vector for the diffraction grating is different, it is important to ensure that the diffraction scattering of the grating for light beams with out-of-range wavelengths is sufficiently weak. Otherwise, the presence of gratings with different grating vectors may result in additional diffraction orders, which may result in shifted or colored ghost images, which are generally undesirable in AR or VR display systems.

Methods that engineer the most dependence on wavelength use resonant scattering materials, such as quantum dots or nanostructured metallic features, to induce surface plasmon resonances. It includes doing.

In other embodiments, multiple IRGs may have identical grating vectors and may be stacked very close to each other such that the projected light is located within the coherence length. In some applications, the projected light will be an LED-based light source and will have a wavelength range of 450 nm to 650 nm and a spectral width of 10 to 50 nm. For materials with a refractive index ranging from 1.5 to 2.0, a coherence length range of 2 μm to 28 μm occurs. In this situation, a composite of multiple IRGs is equivalent to the single multilayer IRG described above and should be treated for analysis purposes such as electromagnetic scattering simulations in IRGs.

In some embodiments, where each pair of input and output gratings is dedicated to a narrow range of wavelengths, or where the projected light may consist of only a narrow range of wavelengths, the y-direction grating vector g _y of the input grating g ₁ and the output grating is It may be advantageous to relax the constraint that they must be identical. In this case, the light beam coupled with cumulative order {0,-1} outside the DWC has its may include additional contributions to the xy-wavevector. This difference can be advantageous in some systems as it allows additional bias to be applied to the output beam compared to that provided at the input. For example, it may be advantageous to have the projection light incident on the input grating such that the center of the viewing field of view is incident perpendicular to the DWC, but the output is tilted horizontally and/or vertically from normal incidence. This tilt can be used to provide a pantoscopic tilt or facial wrap angle for a DWC used as part of a head mounted display.

When used with projection light that covers a wide range of wavelengths, mismatches in g ₁ and g _y in DWC can lead to blurring of the output and color separation of the image as a result of the well-established dispersive properties of the diffraction grating. However, if the mismatch between g ₁ and g _y had been compensated in advance, using other elements, such as additional diffraction gratings between the input gratings of the projector and the DWC, such blurring would have been caused by the mismatch between g ₁ and g _y in other ways. It can be reduced to make it feasible in systems featuring a wider range of wavelengths than would otherwise be feasible.

A variety of methods can be used to fabricate DWCs with multiple gratings, including but not limited to:

i) Multiple surface processing - a method of generating grating elements on the surface of a substrate, such as a glass wafer, to provide two input grating elements overlapping in the xy-plane and/or two output grating elements overlapping in the xy-plane. It can be used on both waveguide planes of planar air waves. Suitable methods for creating grating elements on each surface include secondary processes such as single or multilayer coating, along with nanoimprint lithography of resin or lithographic etching of the substrate or coating on the substrate.

ii) Repetitive surface treatment - The method of forming lattice elements on the surface of a substrate can be used repeatedly to form a layer of lattice structures. For each layer, methods such as nanoimprint lithography of resin or lithographic etching or coating of resin can be used to create the grating element along with secondary processes such as single or multilayer coating. A uniform layer of resin can be applied between each grid layer to provide spatial separation between the grids and a fresh, flat surface for performing new grid structuring steps, typically using the same process each time. By this approach, multiple layers of lattice structures can be formed.

iii) Rigid lamination - Separately prepared rigid substrates, such as glass wafers, can be laminated together using an optically clear adhesive with one or both surfaces each featuring grating elements. When grating elements are included on one or both of the faces bonded together, the adhesive used to laminate the substrates together must have optical properties that provide at least one difference from the grating elements, and the scattering properties of the grating elements must be different from those of the adhesive. It must be guaranteed not to be canceled by index matching with .

iv) Flexbile lamination - Grids can be formed on flexible polymer films using methods such as reel-to-reel nanoimprint lithography. Multilayer grids can then be formed in DWC by laminating multiple layers of polymer film onto a suitable substrate, such as a piece of glass. Each layer of the film may be coated with a resin to provide adhesion and assist in leveling the film.

These methods can be applied together to increase the complexity of lattice elements that can be maintained within a single DWC. Additionally, multiple DWCs, each featuring multiple layers of multiple grating elements, may be used in some display systems.

In all manufacturing methods, it is advantageous if a high degree of parallelism is maintained between the various grid layers, as well as between the outer face of the DWC and the grid layers. This is because if it deviates from the parallel state, additional deviation occurs in the beam path of the projected light. This deviation can degrade the viewing performance of the projected light, such as reducing resolution.

Spatial variation of interleaved rectangular grids.

In other arrangements of the invention, aspects of the IRG may vary with respect to position within one or more regions of the IRG. Modifications of the IRG can be used to change the diffraction efficiency of various orders in relative and absolute terms. Additionally, the dependence of the diffraction orders on the direction, wavelength and polarization of the incident light may vary depending on the position on the IRG.

Aspects for spatial variation include changes in the grating offset vector o _xy , changes in the shape, optical properties and/or material composition of the periodic structures PS1 and/or PS2, and changes in the combination rules used to combine these periodic structures to form the IRG. may be included. In principle, the methods for the design and modification of IRGs described above, as well as other methods for the design of IRGs, can be used within specific sub-regions within an IRG to provide spatial variation of the overall grid. For example, using the method described above to provide differentiation between periodic structures in an IRG, the transformation may be applied to only one of the periodic structures, or aggregated to both periodic structures PS1 and PS2 to differentiate between the periodic structures. It can be applied negatively.

In many arrangements, _it is desirable for the lattice vectors _g

As shown in the previous examples, the shape difference between structures S1 and S2, or the deviation of the grating offset vector from the position required for FSIRG, to vary the diffraction efficiency of the two-eye order, which is more sensitive than the conversion order. Changes in parameters such as may be used. Spatial variation of the IRG may provide advantages in optimizing the IRG for use in DWC, such as some or all of the characteristics listed in Table 3 in latitude 71. For example, it may be advantageous to increase the magnitude of the two-eye orders to compensate for the loss of light leaving the grating when the grating couples out as the light extends toward the edge of the grating. In this way, variation in luminance output with respect to eyebox position and/or gaze angle can be reduced, thereby improving uniformity.

In some arrangements, it may be advantageous for the type of grid to vary depending on the position. This allows certain diffraction orders to be zero, while other diffraction orders can be made relatively large. Figure 40A shows a top view of a portion of IRG 4001. Here, periodic structure PS1 consists of pillar-shaped structures 4002 with a circular profile when viewed in the xy-plane, and periodic structure PS2 consists of pillar-shaped structures 4003 with a square profile when viewed in the xy-plane. It is composed. The height and material composition of the structures are the same. The value of the lattice offset vector is am. By changing the shape of the structures 4002 to new structures 4004 having the same shape as the structures 4003, the IRG becomes an FSIRG (FSIRG) whose two-eye order in Table 2 of FIG. 4005). The IRG area composed of FSIRG does not output light beams, but only has the ability to convert them.

Figure 40B shows a top view of a portion of IRG 4006 comprised of pillar-type structures. Here, the structure 4007 of the periodic structure PS1 and the structure 4008 of the periodic structure PS2 have the same shape and composition, but the lattice offset vector o _xy deviates from the value required for the special cases of FSIRG, VSIRG and HSIR. All non-evanescent diffraction orders for this grating can have non-zero diffraction efficiencies. Lattice Offset Vector By changing to the value of , IRG (4006) becomes FSIRG (4009), and the diffraction efficiency of the two-eye diffraction order in Table 2 of Figure 46 becomes 0. Similarly, the grid offset vector is HSIRG is formed by changing the value of , or the grid offset vector. VSIRG is formed by changing the value of .

To achieve a change in grid type, several aspects of the grid may be changed simultaneously. For example, Figure 40c shows a top view of a portion of IRG 4010 with periodic structure PS1 consisting of pillar-shaped structures 4011 with a circular profile and periodic structure PS2 consisting of pillar-shaped structures 4012 with a square profile. . the lattice offset vector of IRG along with applying a shape change to the structure of the periodic structure PS2 to form structure 4013 that matches the shape and composition of structure 4011. By shifting to , IRG can be changed to HSIRG (4014).

Change between grid types

It is also possible to convert part of the IRG into a one-dimensional grid. FIG. 40D shows a top view of a portion of FSIRG 4015 comprised of a pillar-shaped structure 4016 with a rectangular profile. By extending the pillars so that they merge with each other to form a long, continuous structure 4017, a 1D lattice 4018 can be formed with the lattice vector given by (196).

(196)

In this case, only the BT- . This can help improve the confinement of projected light within a specific region of the DWC, potentially allowing multiple output coupling diffraction events in different regions of the grating with non-zero diffraction efficiencies of two-eye order. . A similar conversion can be used to mix together structures in the x-direction forming a 1D lattice with the lattice vector given by (197).

(197)

Here, only the BT-Y and BRT+Y diffraction orders in Table 2 of Figure 70 have non-zero diffraction efficiencies.

Figure 40E shows the transition from IRG 4019 to a diagonal 1D grating 4020 by extending structure 4021 along the diagonal of the grating. Grid 4020 will have grid vector 198.

(198)

For this grating, only the T-X and UT- Similarly, mixing can be performed along a diagonal mirrored about the y-axis to create a 1D grid with grid vector 199.

(199)

And, here only the T+X and UT+X diffraction orders in Table 2 will have a non-zero diffraction efficiency.

It should be noted that the transition shown in Figures 40d and 40e does not need to start with FSIRG, and a proper transition to a 1D lattice can be achieved using a combination of shape changes such as lattice position shifting and geometric morphing. .

Another type of conversion is to completely remove one of the periodic structures. Figure 40f shows IRG 4022 consisting of pillar-shaped structures 4023 and 4024 for periodic structures PS1 and PS2, respectively. By reducing the size of the structure 4024 of the periodic structure PS2 to 0, a rectangular grid 4025 can be formed. This grating has stronger scattering potential due to the two-eye diffraction orders.

Figure 40g shows IRG 4026 composed of pillar-type structures 4027 and 4028 for periodic structures PS1 and PS2, respectively. By transforming the structures of PS1 so that they are mixed together to form a long continuous structure in the y-direction (4029), reducing the structure of PS2 to zero, a 1D lattice (4030) with a lattice vector given by (200) This can be formed.

(200)

Light beams incident on this grating may be diffracted by the TEAT+X and TEAT-X two-eye orders and the BT-X and BT+X back transition orders in Table 2 of FIG. It will have a diffraction efficiency of Similarly, by applying a mixture of structures 4027 in the x-direction, a 1D lattice is formed with the lattice vector given by (201),

(201)

This will provide non-zero diffraction efficiency for scattering by the STE and TEAT-Y two-eye orders, as well as the BT-Y and BRT+Y back conversion orders in Table 2 of FIG. 70.

It should be noted that all variants of FSIRG, HSIRG, VSIRG and various 1D lattices can be described using the same lattices L1 and L2 of IRG, since they essentially represent special cases of generalized interleaved rectangular lattices.

Figure 40h shows a top view of a portion of IRG 4031 consisting of pillar-type structures 4032 and 4033, respectively, for periodic structures PS1 and PS2. By gradually reducing the size of the structures 4032, 4033 relative to position along one or more directions, a region 4034 will arise where the lattice features exhibit a gradient in size. In general, reducing the size of the grating features reduces the efficiency of non-zero diffraction orders. As a result, this will reduce the visibility of those areas of the grid compared to parts of the DWC without grid structures. Preferably, by applying this change in IRG towards the edge of the grid area in the DWC, there is the advantage of reducing the visibility of the grid area as seen by an external observer.

Typically, this transition occurs at a distance between 1 mm and 10 mm of the defined edge. This is gradual enough to achieve a smooth transition, but not so large that increasing the size of the grid results in additional manufacturing costs.

Alternatively or additionally, a gradual decrease in the height of the nanostructures towards the edges of the lattice region could be applied to achieve a similar effect. For gratings consisting of changes in optical properties due to changes in the material, such as gradients of refractive index, the magnitude of the change in properties can be gradually reduced towards the edges of the grating area to achieve a similar effect.

Example of layout of spatial changes

41 shows a DWC 4101 comprised of a light-transmissive planar substrate 4102, inside which is an input grating 4103 for receiving projected light and coupling it to a waveguide within the substrate, an interleaved rectangular grating. There is an output grid element 4104 based on and divided into multiple sub-regions. These subregions can be characterized for modification of the IRG using methods previously described.

Preferably, all subregions of grating element 4104 are based on the same lattices L1 and L2 of the IRG so that the notable diffraction orders and nomenclature of Tables 1 and 2 can be adopted for all regions. Additionally, in many cases, it is desirable that the lattice configuration of the DWC (4101) is equivalent to that of the DWC (2101). Therefore, input grid 4103 has the same design principles as input grid 2104 and a grid vector g ₁ given by equation (182) and period p _y based on inequalities (187) and (188). Likewise, output grating element 4104 has grating vectors g _x and g _y given by equations (189) and (190), where period p_y is equal to the period of input grating 4103, and period _p It is based on the same design principles and inequalities (191) and (192) as (2105).

The central portion of the grid element 4104 is composed of a 3x3 grid of subregions 4105 to 4113. The sub-areas along the central strips 4106, 4107, and 4018 are composed of IRGs with a small degree of symmetry breaking, so that a portion of the projected light can be output through two-eye orders, especially STE orders. This IRG must provide transition orders, especially T+X and T-X orders. Without transition orders, the beams of projected light tend to follow the central strip of the waveguide, thus distributing the light outward to different parts of the grating and expanding the size of the eyebox. The degree of symmetry breaking can be increased from subregions 4106 to 4107 to 4108 to increase the amount of light coupled out of the waveguide and to compensate for the loss of light due to output coupling and pre-diversion of the light beam propagating along DWC 4101. You can. There are various ways to achieve this. For example, the lattice offset vector may be increased from sub-region 4106 to 4107 to 4108, or geometric morphing may be used to increase the shape difference between structures S1 and S2 of each IRG sub-region. In some configurations, it is advantageous to also increase the diffraction efficiency of the T+X and T-X transition orders. This can be achieved by changing the size and/or height of structures S1 and S2 from subregion 4106 to 4017-4108. This can also help compensate for depletion of light as it propagates along the waveguide.

The strip on the +x side of the 3x3 grid consisting of subregions 4105, 4018, 4111 may also be composed of IRGs. Here, the IRG can be configured to have relatively high diffraction efficiency for the TEAT+X and TEAT-X two-eye diffraction orders, and in particular the main path of the beam entering these sub-regions is the { of the output grating element 4104. 1,-1} There is a high probability of passing the cumulative order. Likewise, the strip on the -x side of the 3x3 grid consisting of subregions 4107, 4110, 4113 consists of IRGs configured to have relatively high diffraction efficiencies for the TEAT+X and TEAT-X two-eye orders, in particular The main path of the beams entering these sub-regions is likely to pass through the {-1,-1} cumulative order of the power grating element 4104.

Alternatively, in other configurations subregions 4105, 4107, 4108, 4110, 4111, 4113 have the grid vector given by equation (200) It may be a 1D grid with . In this case, the two-eye orders of TEAT+X and TEAT-X can be made relatively large without interference from other conversion orders except for the x-direction inversion orders BT+X and BT-X.

In some configurations, subregions 4114, 4115 are outside the projected eyebox of the system. Light reaching this area is potentially wasted, so there is no advantage in providing two-eye orders. These regions are given by the grid vector given by equation (196) By configuring a 1D grating with These orders direct the light beams toward the interior of the grating, allowing them to be usefully out-coupled from the grating, thereby increasing the efficiency of the system. Because there are no two-eye orders, the diffraction efficiency in this region can be very large to efficiently return light into the grating, without fear of inducing large non-uniformities in the output of the grating element 4104. Sub-region 4114 is optimized to particularly favor the BT-X order, and sub-region 4115 is optimized to particularly favor the BT+X order. In other configurations, subregions 4114, 4115 are comprised of HSIRG, which also provides a mechanism for providing back-turn orders in the x-direction.

Similarly, in some configurations, subregion 4116 is outside the projected eyebox of the system to provide back transition orders BT-Y and BRT+Y without loss of light in any of the two-eye orders. The grid vector given by equation (197) It can be composed of a 1D lattice with . These orders can be usefully out-coupled from the grating by turning the light beams toward the inside of the grating. Alternatively, subregion 4116 may be comprised of VSIRG, which also provides appropriate inversion orders in the y-direction.

One of the advantages of the diffraction orders provided by IRG is that fewer cumulative orders corresponding to waveguide propagation are allowed compared to other systems based on 2D gratings such as WO 2018/178626. This can improve the efficiency of structures designed to bounce beams back from the periphery of a grating region, as each region typically only needs to be associated with light propagation due to a single cumulative order of 2D grating elements based on IRGs.

The sub-region 4117 is located at the periphery of the grid. In some configurations, this area is outside the projection eyebox of the system and the grid can be configured to have a structure that fades out in a uniform manner as shown in Figure 40H. In this way, the edges of the output grating element 4104 can be softened, making its appearance within the DWC less noticeable to external observers.

Figure 42 shows a DWC 4201 consisting of a light-transmissive planar substrate 4202 with spatially varying grating elements 4203. Preferably, grating element 4203 is an IRG composed of grating vectors based on similar principles as used in DWC 2101. The IRG can couple light outside the DWC for observation and thus couple projected light into the waveguide through diffraction orders that have opposite signs to the out-coupled orders. Typically, the diffraction efficiency of this coupling is relatively low as it is required for effective pupil replication and eyebox expansion. In some arrangements, subregion 4204 is configured to provide efficient coupling of light through diffraction orders propagating generally in the +x, -x, and +y directions. Once coupled to the DWC, such light beams will propagate to the remainder of the grating region 4205, which can be configured as an IRG with optimized diffraction characteristics to serve as the output element of the DWC. Region 4205 need not be uniform and may include many sub-regions with different properties to provide advantageous properties. For example, the regions of the -x and +x sides of subregion 4204 may be comprised of a 1D grid that will preferentially transition according to equation (198) on the -x side and equation (199) on the +x side, respectively. , each preferentially turning the light beam, generally towards the +y direction, as needed for useful output to the eyebox of the viewing system. In this way, a single lattice element can provide all the functions required for a DWC for use in an AR- or VR-display system.

An interpolation method for spatially varying transitions in interleaved rectangular grids.

As in the examples described above, rapid changes in a grating element containing several sub-regions with different configurations of the IRG may cause undesirable effects depending on the magnitude of the change. For example, changes in the scattering properties of the grating may give external observers a tile- or mosaic-like appearance, which may be undesirable in the appearance of the product. The projected light contributing to the observation at a particular location within the eyebox, and the viewing angle within the system, must come from a corresponding patch of the DWC's output elements. This patch has a size, shape, and location determined by projecting the entrance pupil of a viewing system (e.g., an eye) backward onto the output element along the gaze path. As the sub-regions illuminate different portions of the observed field of view, undesirable non-uniformities in brightness and/or color may be experienced by the viewer as the viewer's observation moves with position within the eyebox. . Sudden changes in grating properties can also result in changes in the wavefront of beams overlapping those transitions. This can have undesirable effects, such as reducing the sharpness of focus that can be achieved with such a beam.

Various methods can be used to mitigate these effects. One way is to reduce the size of the change by subdividing each subarea into several smaller subareas. The grid of each of these sub-regions can be designed to have structures and configurations that provide a more gradual change in scattering properties compared to the grid of adjacent sub-regions. For example, each of the nine sub-areas within the 3x3 grid of sub-areas of the grid 4104 may be divided into a 3x3 grid, creating an overall grid of 9x9 sub-areas. This subdivision can be applied repeatedly to form a larger number of subregions, with the ultimate limit being the subregion corresponding to a single unit cell.

In essence, the refinement process, followed by adjustment of the grating properties in new subregions to provide a more gradual transition in the scattering properties, is a form of interpolation method consisting of the optical structures of the diffraction grating. A wide range of interpolation methods, including parametric and non-parametric techniques, can be applied to this task.

If all sub-regions are based on the same lattices L1 and L2, and the material composition of the lattice does not differ between sub-regions, in principle, the change of the lattice offset vector o _xy of the IRG in each sub-region and/or the A wide range of transitions can be achieved by changes in the conformation of the structures S1 and S2 of the IRG. Depending on how the shape of the grid varies, the latter may be possible through the geometric morphing method described above or through simple methods based on changes in the size, orientation, height and/or blaze of the structures. As shown in Figure 23, for structures created based on parametric description, intermediate forms can be created by interpolation of parameter values for positions.

In one approach, the design of the grid is a series of xy-coordinates It can be stipulated in . Points may or may not lie on a grid, but generally they should not all be on a line. Interpolation between these individual positions is used to define the design at each unit cell based on the unit cell's coordinates. If there is a set of defined points on the grid, methods such as bilinear and bicubic interpolation can be used. If the points are not on a grid, methods based on thin plate splines, Kriging, polynomial basis functions and triangular irregular networks using linear interpolation are used. Other methods may be used, including: The scatteredInterpolant function in Matlab® provides an implementation of linear interpolation for irregularly distributed data points. Outside the convex hull surrounding the points, extrapolation methods can be used to specify the required design. This extrapolation can be chosen to anchor the properties at the edges of the convex hull, or various methods can be used to generate new values, such as linear extrapolation.

Interpolation and extrapolation can be performed for any parameter values that describe the design of the IRG in the region including the lattice offset vector, the values governing the size and shape of structures S1 and S2, and the parameters governing the transformation.

For example, Figure 43 shows a cross section of a grid where the columns are indexed with the integer i and the rows are indexed with the integer j. Points on the grid correspond to xy-coordinates placed on the grid in the spatially varying xy-plane of the IRG. index is the coordinate given by (202) has

(202)

here is the origin of the grid, P is the period of the grid in the x-direction, and Q is the period of the grid in the y-direction. The periods P and Q should not be confused with the periods p _x and p _y of the IRG, which will generally have much smaller values. Advantageously, P and Q may be integer multiples of p _x and p _y respectively. At each point of the grid, a scalar value that requires interpolation is defined. If, using the s(i,j) notation, the grid , the bilinearly interpolated value s(u,v) at an intermediate point with coordinates (u,v) can be found by the following procedure:

i) and The i and j values for the nearest grid point are calculated with formulas (203) and (204).

(203)

and

(204)

i) ii) Next, the parameters α and β are calculated by formulas (205) and (206).

(205)

and

(206)

iii) Next, the double interpolation value s(u,v) is given by (207).

(207)

If the point (u,v) is outside the grid, the value s(u,v) can be fixed to the value at the edge of the grid, or extrapolated based on the x- and y-gradient of the point on the grid closest to the point. there is. It is desirable to avoid extrapolation, as this may result in parameter values being outside the range of valid values. Alternatively, the grid can be defined to have a larger range than the final grid design, to avoid extrapolation from the physical extent of the actual grid.

Any number of parameters describing the IRG can be interpolated by this approach, by treating each parameter as a separate grid of scalar values and performing interpolation on these values. For example, for a grating design where a change in the lattice offset vector is used to control the intensity of the diffraction orders, interpolation may be applied separately to the x- and y-components of the lattice offset vector. In this way, various variations of shape, lattice offset and even lattice configuration can all be handled with the interpolation method.

In other approaches, interpolation and extrapolation can be used to provide the desired target values for the diffraction efficiency of the grating for the position. These target values can then be related back to the corresponding designs of the IRG. There are many diffraction orders that may have a non-linear dependence on the direction, wavelength and polarization of the incident beam, so a choice may have to be made as to which diffraction orders and which incident beam conditions are used to provide target values. . For example, a simple approach is to choose a single diffraction order and a single direction and wavelength for the incident beam, perform interpolation on this, and select the value of a single parameter for the IRG at the interpolated position. For example, the diffraction efficiency of the two-eye order shown in graph 2405 is 0.4 It can be used to select s _x values in the range s_x≤0.8. Efficiency values between 0% and 1% can be uniquely related to the s _x value. By constructing an average efficiency measure over a desired range of incident beam directions and/or wavelengths, a range of incident beam characteristics can be taken into account. These averages may be weighted to give more importance to particular directions and/or wavelengths of the incident beam.

For grating designs with multiple parameters, it may be desirable to create multiple targets for diffraction efficiency at intermediate locations. This can be done by examining multiple diffraction orders to calculate average performance and/or defining characteristic ranges of multiple incident beams. In this approach, an interpolation can be performed on the values derived by each range of incident beam characteristics for each diffraction order under consideration. The resulting values of diffraction efficiency can be used to select a grating design.

In general, it may not be possible to design to provide exactly the desired diffraction efficiency. In this case, it may be desirable to use multi-objective optimization to find or select a grid design that provides an optimal approximation of the target. For example, one approach may be to select a variation of the grating design based on the minimum least squares difference with respect to the various target diffraction efficiencies desired. If a particular diffraction order and/or a particular range of incident beam parameters are more important, different contribution weights may be used. This optimization may be limited to designs with a similar shape to the surrounding grating, differing in details such as grating offset or structure size, or it may allow for a broader exploration of grating designs to provide the desired diffraction efficiency.

As previously explained, geometric morphs can be used to create a form that represents an intermediate form between two different forms. When interpolating across a grid with two-dimensional spatial transformations, it may be necessary to combine contributions from two or more types. For example, equation (207) shows that bilinear interpolation of a two-dimensional grid typically combines four values at points on the grid to form each interpolated value. To extend this concept to geometric morphing, we need a way to combine the four shapes together.

A similar method to bilinear interpolation is to reduce combinations of shapes into successive pair-wise geometric morphs. Here we can assume that the form of some part of the IRG, such as structure S1 or S2, is defined on the grid of points shown in Figure 43 with the coordinates of the grid points defined by equation (202) and exponents as previously described. For convenience, we use the same notation (i,j) as before, except that this is a grid point rather than a scalar value. Please note that it represents the form in . As explained previously, morphs can be governed by parameters that describe the transition from one form to another. For convenience, we will represent the morph using function-based notation, so that if A and B are two end-point shapes, and γ is a parameter governing the morph as previously described, then the morph shape C is given by (208) given.

(208)

Here we , and It should be noted that it is based on . As previously mentioned, there are a number of algorithms described in the public domain that can be used to perform actual morph functions, which will be defined in detail here to illustrate the approach required for interpolation of a defined shape at points on a grid. no need. Using this definition interpolated in coordinates (u,v), s(u,v) can be calculated using the approach below.

i) The values of i, j, α, and β are calculated according to equations (203), (204), (205) and (206).

ii) A new form S _A is created by morphing between s(i,j) and s(i+1,j), and α is used as a parameter that governs morphing according to (209).

(209)

iii) A new form S _B is created by morphing between s(i,j+1) and s(i+1,j+1), and α is used as a parameter that governs morphing according to (210).

(210)

iv) The final interpolated form s(u,v) is generated by morphing between S _A and S _B , and β is used as a parameter that governs morphing according to (211).

(211)

We can extend this result to show that the result comes from successive applications of the morph function (212).

(212)

Figure 44 shows an example of this process, where shapes 4401 and 4402 are morphed to create shape 4403. Likewise, shapes 4404 and 4405 are geometrically morphed to form shape 4406. Finally, shapes 4403 and 4406 are geometrically morphed to create shape 4407.

In fact, this approach is equivalent to the approach that can be used to derive equation (207). Linear interpolation between the values s(i,j) and s(i+1,j) for parameter α derived according to equation (205) gives the value (213).

(213)

Similarly, linear interpolation between the values for parameter α, s(i,j+1) and s(i+1,j+1) gives the value (214).

(214)

Performing a linear interpolation between the values S _A and S _B for parameter β derived according to equation (206) gives the value (215),

(215)

This extends to (216).

(216)

The expression for S _C in equation (216) is the same as s(u,v) given in equation (207). This shows the conceptual equivalence between bilinear interpolation of numerical values and interpolation of forms using geometric morphing.

Function-based method for spatial variation of interleaved rectangular grids

Another approach to describe the spatial variation of the IRG is to use a function of the (x,y)-coordinates in the xy-plane of the IRG, including parameters that describe the shape of the structures as well as the lattice offset vector of the IRG. It explains how parameters change depending on position. For example, the description of the periodic structures PS1 and PS2 given by equations (130) and (131), respectively, can be extended to include position dependent parameters and written as (217) and (218).

(217)

and

(218)

Here, the terms a ₁ (x,y) and a ₂ (x,y) are vector functions of positions where each element of the vector corresponds to a parameter used to describe the form of structures S1 and S2, respectively. In this way, the definitions of the structure functions S ₁ () and S ₂ () are extended to express the input parameter values explicitly, whereas previously, for structures that did not vary with position, the parameters were implicit within the definition of the function itself. could be included. Here, a ₁ (x,y) and a ₂ (x,y) are evaluated at points in the lattice L1 with coordinates given by (ip _x ,jp _y ), which means that the parameter values are Guarantee consistency. Equation (218) also shows that the x- and y-components of the lattice offset vector can be expressed as scalar functions depending on the points of the lattice L1 of the IRG.

Applying a similar use of the extended definition to the volume description of the periodic structures PS1 and PS2 given by equations (176) and (177), (219) and (220) are given.

(219)

and

(220)

and , As well as and Each element of is a scalar function of position. In principle, any type of function that produces a valid, finite value at each evaluation point can be used. For some expressions, it may be advantageous to construct each scalar function from a set of basis functions. For example, if B _i (x) is a series of one-dimensional basis functions described by exponent i, the two-dimensional scalar function F (x, y) can be composed of (221).

(221)

where N ₁ and N ₂ are limits on the x- and y-dependent terms allowed for F(x,y), and b _ij is B _i (x) B _j (y) for F(x,y) This is the coefficient for the contribution of the term. The appropriate form for the basis function is a simple polynomial , Chebyshev polynomials of the first and second kind, Legendre polynomials, or additional Fourier series for which an additional set of parameters of period T _and phase i must be defined. Includes. For some expressions based on polynomials, it may be advantageous to use a normalization constant to control the range of (x,y) values applied to the basis function to avoid numerical stability issues associated with high-order terms. If n _x and n _y are normalization constants, the appropriate modification of equation (221) is (222).

(222)

In general, the values of n _x and n _y are relative to the dimensions on the grid. and This happens.

Two-dimensional basis functions, such as Zernike polynomials, can also be suitable expressions for F(x,y); Typically, they will also use normalization forms for x and y values. Alternatively, the scalar function may be constructed piecewise, such as a piecewise polynomial, or as a two-dimensional non-uniform rational B-spline (NURBS) surface.

In another approach, any scalar function that describes parameter values or lattice offset components can be used to interpolate between a series of points defined in the xy-plane in a similar manner as described previously.

In general, the function used to describe each of these scalar functions and the coefficients on which such function depends need not all be the same for the various parameters described by the function. Additionally, multiple scalar function types can be combined simultaneously in a single, global scalar function that describes parameter values or lattice offset components.

The functional definition can also be used to apply other aspects to generate structures of IRg. For example, a geometric modifier can be made position dependent, and that position dependence is accounted for using the same method as described here.

Many function definitions depend on coefficients or other parameters to describe the function. In many cases, the choice of the values of these parameters, such as the IRG's output elements, is important in determining the performance of the IRG in a given application. In the intended application, if the performance of the IRG can be measured in one or more numerical values, various optimization techniques can be used to guide the selection of parameter values.

In some approaches, simulation can be used to calculate the output from a DWC using IRG, where the input consists of an ensemble of beams with uniform brightness over a defined viewing field of view and a choice of wavelengths. The criteria listed in Table 3 of Figure 71 can be used to inform the calculations of these simulations, which provide a measure of the performance of the system. For example, the average output luminance can provide a measure of the efficiency of the system, and the change in output luminance can provide a measure of directional uniformity. Depending on the optimization method used, these values can be combined together using an appropriate function or kept separate. A common approach in optical design is to combine various aspects of performance in an overall scalar merit function to measure the overall performance of the system. Linear weighting factors, or other methods, can be used to expand and emphasize the importance of various metrics to measuring the overall performance of the system. In general, such calculations are often arranged so that the minimum value represents the best performance, but this need not be the case. There are a wide variety of optimization methods that can be used to find a set of values to specify the spatial variation of the parameters that govern the spatially varying IRG. These methods include the steepest-gradient method, quasi-Newton method, Nelder-Mead method, genetic algorithm, brute force search algorithm, simulated annealing algorithm and these techniques. Hybrid methods that combine two or more of these include, but are not limited to.

Simulations of a DWC with a spatially varying IRG will typically use a combination of ray tracing methods to calculate the effect of the various beam paths possible in the IRG along with wave-based calculations to calculate the scattering properties of the IRG. For spatially varying IRGs, scattering properties may require calculation at each location in the grid. If the changes in the lattice are sufficiently gradual, it is possible to invoke periodic boundary conditions over a single unit cell and calculate the scattering properties based on them, providing a reasonable approximation. This greatly reduces the required computational burden. For beams where the distance between abrupt changes is much larger than the wavelength of light and much larger than the unit cell of the grating, abrupt changes in the grating may be calculated using this approach.

If the scattering properties of the IRG vary with position in a continuous and well-behaving manner, interpolation methods can be used to further reduce the computational burden. Here, the scattering properties of the grid can be calculated at various reference positions, and interpolation is used to calculate the scattering properties at intermediate positions. Typically, this interpolation will be performed for values corresponding to a single diffraction order in a single direction of an incident beam with a single wavelength.

Various methods for spatial variation can be selectively applied to different subregions of the IRG and combined together. For example, function-based methods can be used to account for parametric spatial changes within an IRG sub-region and combined with interpolation methods to transform other sub-regions of the IRG.

Phase compensation and modulation method for interleaved rectangular gratings

Unless otherwise specified, all phase shifts should be assumed in radians in this description. In addition to changing the magnitude of different diffraction orders, spatial variation of the IRG can also affect the polarization-dependent phase shift imparted to the electric field of the diffraction orders. Such phase variations can affect the wavefront of the scattered light beam which can degrade the image sharpness that can be achieved for the projected light beam. As previously explained, there are generally multiple paths through which projected light beams derived from the same input beam can be output at a particular location in the DWC using an IRG as the output element. If these paths acquire different phase shifts due to non-zero diffraction orders in the spatially varying IRG, complex interference effects may occur when the beams recombine, resulting in reduced output uniformity.

In practice, it is desirable to keep the non-plane phase variation across the light beam or general viewing pupil to within a small fraction of 2π. For some systems, it has been found desirable to limit the extent of phase departure to π/2 in the plane across the 2 mm diameter fracture front. For systems targeting lower image resolutions, a phase shift of less than π/2 in a 1 mm diameter wavefront (or part thereof) may be acceptable. For high-resolution systems, a phase shift of less than π/2 may be required in a 4 mm diameter wavefront (or part thereof). Depending on the nature of the phase departure, it may be advantageous to construct a statistical measure of the phase departure across the wavefront. A common measure is the root-mean-square (RMS) of the phase departure from the plane wavefront, where the rms phase departure is less than π/4 over a 2 mm diameter wavefront, or for high-resolution systems over a 4 mm diameter wavefront. It may be desirable to ensure that is less than π/4 over .

For some configurations of spatially varying IRGs it may be advantageous to include some form of phase compensation to balance the variation in phase imparted to the IRG diffraction orders. One way to achieve this is to introduce an entire position shift of the IRG lattices into the area of the IRG. For example, assume an IRG with a lattice function for lattices L1 and L2, respectively, given by (223) and (224).

(223)

and

(224)

Shifting these lattices by _a distance _d

(225)

and

(226)

In this way the position shift of the IRG's lattice does not affect the orientation of the various diffraction orders. However, when scattering from an IRG composed of lattices described by equations (225) and (226), the order Comparing the diffracted beam of with the scattered beam from another identical IRG consisting of lattices described by equations (223) and (224) will yield an additional phase shift of (227).

(227)

Note that only non-zero order scattering causes this phase shift effect.

If we create d _x and d _y scalar functions in (x,y)-coordinates and call them lattice shift functions, the phase shift can be changed in the IRG. Therefore, the position dependent phase shift is given by (228).

(228)

When used with lattice functions, it is convenient to evaluate the lattice shift function at the lattice L1 point. Therefore, the lattice functions for lattice L1 and L2 can be written as (229) and (230), respectively.

(229)

and

(230)

Here, both lattices L1 and _L2 are collectively shifted by ( _d do.

Instead of adding a position-dependent shift to the IRG's constituent lattice, in some deployments it is desirable to apply a position-dependent shift to the lattice itself. This can be achieved by shifting the (x,y)-coordinates of the IRG representation by coordinate transformations (231) and (232).

(231)

and

(232)

For example, if I(x,y) is the IRG surface function, then the modified IRG surface function after the shift is given by (233).

(233)

Essentially, equation (233) produces a new grid surface function by distorting the coordinate system of I(x,y) indicates that is formed. This may result in distortion of the IRG structure as well as the distribution of lattice points, although in the case of small shifts the modification of the structures may have a negligible effect on the diffraction efficiency of the structures.

It is important to note that the transformations in equations (231) and (232) can be applied to any description of the lattice, not just those that can be expressed as surface functions. This is an additional step between (231) and (231) and ( The necessary distortion will be achieved by introducing the transformation 232). This distortion can be applied at various stages depending on the task at hand. For example, when creating a voxel-based representation of a grid, the voxel coordinates may be transformed according to (231) and (232), and the resulting shifted coordinates will be referenced to the structure to determine the voxel properties at that point. It is used to

Preferably, when used with transformations (231) and (232), the functions d _x (x,y) and d _y (x,y) should be continuously differentiable (class ), which means that these functions and their first derivatives with respect to position are also all continuous. This is to avoid discontinuities or other features of the grid that may cause difficulties when trying to realize the grid in the physical world.

The phase shift introduced by transformations (231) and (232) for small changes in x- and y-coordinates is given by equation (228). Here, small means that the relative size of the unit cell after coordinate transformation does not deviate from the size of the unit cell before transformation. Generally, a deviation of less than 0.1% in the x- or y-direction is desirable, but larger deviations may be acceptable in areas where rapid changes in the lattice are brief. Short here means much smaller than the pupil size of the system, typically much smaller than 1 mm. In this situation, the function and has a similar effect whether used to shift the underlying lattice position of the IRG representation or to distort the (x,y)-coordinates of the IRG representation. This allows the designer to choose how to implement these shifts within the IRG, dictating whatever is best suited to the representation used to describe the IRG.

Phase compensation at a given location on the lattice can be set according to changes in phase shift resulting from spatial changes in the IRG. In general, since the phase shift resulting from a change in IRG depends on the diffraction order and direction of the incident beam, it may be impossible to determine the exact value of phase compensation required at a given location. In this case, the average phase shift from the lattice can be calculated based on the most important diffraction order and incident beam direction at a given location. Since phase compensation is required, the d _x and d _y values can be set accordingly.

In some embodiments, it may be desirable to intentionally induce phase shifts between different beam paths, rather than attempting to compensate for phase shifts that occur as a result of spatial variations. In this case, the goal is not to ensure that all beams are coherent with each other, but rather to check whether they interfere with coherent interference effects. This method is particularly applicable when there are a large number of beams contributing to the output beam, as each can potentially obtain a phase shift with little correlation to the other beams. Quasi-random phase mixing between many beams means that neither constructive nor destructive interference is particularly favored and the output from these IRGs should be much less sensitive to these interference effects.

This is particularly relevant if there are other sources of variation in the DWC that may cause additional phase changes between beams taking different paths through the DWC. For example, small changes in DWC substrate thickness due to manufacturing tolerances cause changes in the optical path length, which can cause interference effects that cannot be accounted for by design but significantly disrupt the uniformity of the IRG output.

To achieve this arrangement, the _{lattice shift} functions d However, rapid or abrupt _changes in _d Any changes should not be too extreme, as this may result in undesirable effects on the projected light output of the same IRG. Accordingly, in some configurations, maximum values for the x- and y-gradient magnitudes of d _x (x,y) and/or d _y (x,y) are set to minimize unwanted optical degradation. It is desirable.

The maximum gradient depends on wavelength, lattice pitch and diffraction order, and can be set by inequalities (234) and (235).

(234)

and

(235)

Here, ∇ is the vector gradient operator, here restricted to the xy-plane, and can be written in row vector form (236).

(236)

Coefficients of inequalities (232) and (233) has a value known as the maximum perturbation to the wavefront across the beam that is considered acceptable. The value of varies with various configurations or low-resolution systems. suitable for In many systems, the diffraction orders used in inequalities (234) and (235) are would.

It is important that the value of η should not be too small or the phase shift too small so that the induced phase shift does not have a significant effect. In the case of quasi-random distributions of phase shift effects, it may be useful to characterize the magnitude of the variation required in statistical terms. In some configurations, it may be desirable to calculate the average phase shift at each location in the IRG over a circular area centered at that location and typically 2 to 4 mm in diameter or 1 to 6 mm in diameter. The diameter of the circle centered at spanning Average phase shift versus diffraction order can be obtained by the polar integral method of (237).

(237)

Typically, the diameter w is equal to the pupil size of the observer or the pupil size of the input beam of projected light. In many deployments, calculated for the required area of the IRG. It may be advantageous to satisfy the standard deviation of (238).

(238)

Here, STD(A(x,y)) represents the calculation of the standard deviation of the spatially dependent quantity A(x,y) for a defined region of interest. also, If the average of the gradient magnitude satisfies (239), it can be advantageous as it can help ensure that the phase variation is fast enough.

(239)

Here, STD(A(x,y)) represents the calculation of the standard deviation of the spatially dependent quantity A(x,y) for a defined region of interest. It was found that the coefficient ζ must satisfy ζ>0.1 or ζ>0.25 or ζ>0.5 to ensure a phase shift of sufficient magnitude and variability induced across the IRG. For these IRGs, it is desirable that the gradient constraints of inequalities (234) and (235) are still respected. For practical applications, it is necessary to specify the diffraction order for the phase shift function. In many cases, It was found that setting is appropriate for providing effective constraints.

The shift function d _x (x There are many suitable expressions that can be used for ,y) and d _y (x,y). Other expressions include Zernike polynomials, piecewise polynomials, and NURBS surfaces.

Properly put _, designing lattice shift functions _d . For example, when using a Fourier series representation, it may be desirable to limit the number of terms so that the shortest spatial frequency is similar to the size of the viewing pupil. This can help limit the gradient of a scalar function. The parameters of the representation can be set in a variety of ways, including the use of a pseudo-random number generator. This approach can be applied iteratively to ensure that the various constraints and inequalities described above are respected.

If the expression of the IRG uses a construction principle based on lattice functions according to equations (229) and (230), d _x (x,y) and d _y (x,y) do not need to be smooth and continuous functions. This allows the use of other methods for the functions of d _x (x,y) and d _y (x,y) in addition to those disclosed previously. For example, a method based on a recursive refinement of a grid of grid planes followed by deviation by pseudo-random numbers can be used. In this situation, the gradient constraints of inequalities (234) and (235) need not be respected. Instead, we use the Lattice branch at and We only need to be interested in the value of . Afterwards, between adjacent lattice points according to below and You can set constraints on the maximum change in the value of:

(240)

(241)

(242)

and

(243)

In general, the coefficient η is has a value of, or in low-resolution systems It was found that it is desirable to The most important diffraction orders generally satisfy |m _x |=|m _y |=1.

The requirements for the average phase shift and the gradient of the average phase shift given by inequalities (238) and (239) are in principle applicable. However, to calculate these quantities the evaluation of the phase shift must be done at the lattice point It should only be performed in This will convert the integral to the sum of the lattice points within a circular area of diameter w centered at position (x,y). Therefore, the resulting expression for the average phase shift is given by (244).

(244)

Here, the function rect(x) is defined as equation (146). Strictly speaking, the gradient of this function is the lattice point. It may not be smooth due to discrete features that may or may not be present within the circular aperture used to evaluate . Problems can arise when applying the gradient operator required by inequality (239). This is achieved by a finite difference spanning at least several lattice cycles in the x- or y-direction, as required in the differentiation direction. This can be relaxed by using numerical differentiation to calculate the gradient of . for example, The appropriate definition of the gradient operator applied to can be given as (245).

(245)

Here, the finite differential parameters Δ _x and Δ _y are the distance of at least several lattice cycles, in the x- and y-directions respectively. For example, suitable finite differential parameters may be Δ _x ~10p _x and Δ _y ~10p _y , or more.

In some arrangements, it may be desirable to allow rapid changes in the shift functions d _x (x,y) and/or d _y (x,y). Alternatively, it may be desirable to allow rapid changes in the shift function over a short region that is much smaller than the size of a typical light beam. In this situation, the gradient constraints of inequalities (234) and (235) are no longer appropriate. Instead, a useful quantity is the root-mean-square (rms) phase shift (246).

(247)

In general, the diameter w used to evaluate equations (247) and (248) will be smaller than the pupil size of the observer and, through this modification, the beam size of the projected light entering the DWC featuring the grating. At any position on the grid where light beams can interact and be output towards the observer By setting a limit to , limits on image degradation can be imposed. This can be expressed by requiring the rms phase shift to satisfy (248).

(250)

Here, k is a coefficient that determines the degree to which degradation of image performance (fidelity) can be tolerated. For low resolution systems, a value of k=0.5 may be appropriate, while for medium resolution systems a value of k=0.25 may be required. For high-resolution systems, smaller values in the range 0 ≤ k < 0.12 may be necessary to avoid significant degradation of image quality. A smaller k reduces the extent to which significant phase differences can be engineered into the layout of the grid. To ensure that sufficient phase shift is generated, the conditions given by inequalities (238) and (239) can still be applied to the grid satisfying inequality (248). To avoid artifacts arising from the overlap of discrete lattice points with the measurement circle of the Rms phase shift, a finite differentiation method over several lattice cycles is used. The x- and y-gradients of can be evaluated. This means that equation (247) is It may be particularly suitable for systems used to find .

Accordingly, a flexible range method for imparting position-dependent phase shifts to non-zero diffraction orders of IRGs has been established.

Another way to induce a path-dependent phase shift for various beams propagating through the DWC is to introduce small changes in the thickness of the DWC. This transformation can be achieved in a variety of ways. For IRGs using a surface relief structure, a base layer of variable thickness can be added beneath the surface relief structure. Another approach is to change the thickness of the DWC's substrate so that the surfaces are no longer significantly parallel. This can be achieved by a variety of methods, including manufacturing the substrate with intentional thickness variations or applying a transparent resin layer of variable thickness to one of the outer surfaces of the substrate. This resin layer may be the same as that used in the surface relief structure of the appropriate IRG.

Preferably, any thickness changes in the DWC will be relatively small, typically less than 10 μm, as well as gradual. As the thickness t of the DWC increases, the optical path length for the beam between successive bounces within the waveguide increases to 2t cosθ, where θ is the angle of incidence of the beam with respect to the waveguide surface. Given that the thickness change is a scalar function of position t(x,y), the additional phase obtained after double reflection in the waveguide can be written as (249).

(249)

Here, n is the refractive index of the variable thickness medium, which will generally be close to the refractive index of the substrate. If the incident angle of the beam changes from θ ₁ to θ ₂ due to a non-zero diffraction order of the beam, the obtained phase is given by (250).

(250)

Unlike the position shift of a lattice, a phase shift occurs due to a change in thickness whenever double reflection of the waveguide beam occurs. Phase shifts due to thickness changes can accumulate faster than phase shifts due to grid position shifts.

Changes in thickness must be associated with changes in parallelism between DWC surfaces. These changes cause the waveguide beams of projected light to tilt or cause high-order wavefront changes, resulting in loss of image clarity, color separation, or deterioration of optical performance due to distortion. To control this effect, it may be advantageous to limit the magnitude of the gradient of t(x,y) to satisfy (251).

(251)

Here the coefficient is That's it . To achieve the desired effect, the phase shift ϕ _t (x,y) should have statistical properties similar to those observed for the phase shift due to the lattice shift function above.

There are many possible uses for the scalar function t(x,y), including using basis functions along the lines of equation (221), such as simple x- and y-polynomials, Chebyshev polynomials, Legendre polynomials, and Fourier quadratics. There are appropriate expressions. Other expressions include Zernike polynomials, piecewise polynomials, and NURBS surfaces. Methods similar to those used for the lattice shift function can be used to appropriately construct a representation of t(x,y) with the required properties.

Although aspects of the disclosure have been described in detail, it will be apparent that modifications and variations may be made without departing from the scope of the aspects of the disclosure as defined in the appended claims. Since various changes may be made in the above configurations, products, and methods without departing from the scope of the aspects of the present disclosure, all matters included in the above description and shown in the accompanying drawings should be construed in an illustrative sense and not a restrictive sense.

Reduced Rainbow Artifact IRG

Unwanted artifacts in the output image of the AR display may occur due to external light sources incident on the waveguide. 45 shows an exemplary waveguide 4501 having an input grating 4512 and an output grating 4514 that take the form of a diffractive waveguide combiner (DWC). Shows a side view. Light 4502 is incident on the input grating 4512, couples to the waveguide 4501, and propagates by total internal reflection at the opposing surfaces of the waveguide toward the output grating 4514, where the light Some may be diffracted to the viewer in the form of diffracted light 4504. The angle of the diffracted light 4504 output from the output grating 4514 is such that the light 4502 is connected to the input grating 4512. It will be an angle that is a mirror reflection of the angle of incidence.

Figure 46 shows the same waveguide 4501 of Figure 45, but with image bearing light 4502 from the projector hitting the output grating 4514 at an angle of incidence within the range of angles incident on the input grating oil 4512. Indicates the presence of incident external light 4508. In this scenario, light 4508 from an external source will couple to waveguide 4501, undergo total internal reflection, and diffract out of waveguide 4501 upon re-interaction with output grating 4514. Because the light 4508 from the external source and the subsequent diffracted output light 4516 are at the same angle, they do not cause unwanted effects in the image viewed by the user.

However, Figure 47 shows a scenario where light 4508 from an external source is incident on the input grating 4512 at an angle outside the range of angles at which it is diffracted into TIR. In this scenario, light 4508 from an external source will be diffracted by the output grating 4514 at an angle less than that required to achieve total internal reflection. Diffracted light 4510 from an external source will exit the waveguide 4501 and be directed toward the viewing area 4516 formed by the waveguide 4501, i.e. the eyebox. This will cause unwanted rainbow artifacts in the eyebox.

These unwanted rainbow artifacts are problematic for augmented reality (AR) and virtual reality (VR) devices because they can affect the quality of the user's overall visual experience. In particular, this effect is difficult to avoid because external light sources are common in many use cases for AR devices. The most problematic light sources are typically above the end user and include the sun if the AR device is used outdoors and electric lighting if used indoors.

There are a variety of techniques that can be used to reduce unwanted rainbow artifacts in output images and fields of view. One way to mitigate rainbow artifacts is to reduce the pitch of the optical structures that form the output grating. This diffracts the rainbow artifacts through a larger angle, causing most of the diffracted rainbow artifacts to miss the design eyebox. This can be accomplished by increasing the refractive index of the material or reducing the pitch of the nanostructure by applying a wrap angle. Rainbow artifacts can also be reduced by reducing the size of the grid, which reduces the range of angles at which the rainbow artifacts are captured by the eyebox.

Another way to help reduce rainbow artifacts is to use a square or rectangular lattice rather than a hexagonal lattice for the output grating, which will reduce the possible diffraction interactions with external light interacting with the grating and causing rainbow artifacts in the eyebox. The number of actions decreases.

The invention described herein is a diffractive waveguide coupler having an output diffraction grating separated into a number of distinct zones, the zones having different diffraction efficiencies. The described output grid ensures improved eyebox uniformity compared to output grids that do not contain spatial variations in grids, unit cells or configurations or do not contain specific regions with different grids, unit cells or configurations. This reduces rainbow artifacts in the output image.

Figure 48 shows a top view of DWC 4520 with input grid 4524 and output grid 4522. The output grating 4522 of this arrangement is formed from an array of optical structures arranged as a hexagonal lattice as disclosed in WO 2018/178626 and WO 2016/020643. DWC 4520 is shown for use in an AR/VR headset in a side injection orientation. Specifically, this means that the input grating 4524 incident a light beam onto the output grating 4522 at a location next to the wearer's eyes (i.e., the The injection is parallel to the line crossing the wearer's left and right eyes). The largest contribution of external lighting to an AR/VR headset comes from light directly above the wearer's head, such as the sun or overhead lighting, as shown in rays 4528 and 4530 in Figure 48. As described above, these rays can cause unwanted rainbow artifacts in the output image and in the user's field of view. The worst-case scenario of external light causing rainbow artifacts for an output grating 4522 with hexagonal symmetry is 120° for the lattice of the output grating 4522, i.e. the line 4526 that intersects the input and output gratings along the y-axis. It is caused by external light incident at ° or 60°.

Figure 49 shows a top view of DWC 4534 with input grid 4538 and output grid 4536. The lattice of the output grating 4536 as shown in FIG. 49 is a rectangular lattice (specifically a square lattice), such as the IRG described herein. As can be seen, the worst case scenario of external light 4540 causing rainbow artifacts in a rectangular lattice (e.g. a square lattice) is for the lattice of the output grating, i.e. the input grating 4538 and the output grating 4536 along the y-axis. is 90° to the line 4532 that intersects . The worst case scenario is less likely to be achieved for a rectangular lattice than for a hexagonal lattice because there are fewer possible diffractive interactions for a rectangular lattice compared to a hexagonal lattice. Therefore, using a rectangular lattice can provide the advantage of reducing rainbow artifacts compared to a hexagonal lattice.

Figures 50 and 51 show k-space diagrams further illustrating the problem of rainbow artifacts due to external light sources incident on the DWC. Figure 50 shows a k-space diagram for a hexagonal lattice described in relation to Figure 48 above, and Figure 51 shows a k-space diagram for a rectangular (in this case square) lattice described in relation to Figure 49 above. It shows. The k-space diagram shows a glass interface 4550 representing the extinction limit and an air interface 4556 representing the TIR limit. The area located within the TIR limits is area 4552, which shows the angular range to reach the eyebox. The incident external light outside the TIR (i.e., the region between 4556 and 4556) is shown at point 4558 at the worst-case scenario angle for each lattice as described above in Figures 48 and 49, and the light output of the output grating is at point 4560. It is shown in This external light creates a rainbow artifact 4551 that is almost completely visible in the eyebox.

Figure 52 shows an example of a DWC 5002 with an arrangement configured to distribute light evenly in the output image, with the goal of reducing rainbow artifacts, especially compared to other types of gratings such as common gratings with hexagonal or rectangular lattice. do. It shows a DWC 5002 consisting of a light-transmissive planar substrate 5004, inside which is an input grating 5006 for receiving the projected light and coupling it to a waveguide in the substrate, based on an interleaved rectangular grating; There is an output grating element 5008 divided into multiple zones 5010 5012 5014 5016. By having different regions, also called sub-regions, the grating can have diffractive properties aimed at reducing rainbow artifacts in the output image.

Preferably, all regions of grating element 5008 are based on the same lattices L1 and L2 of the IRG so that the notable diffraction orders and nomenclature of Tables 1 and 2 can be adopted for all regions. Therefore, input grid 5006 has the same design principles as input grid 2104 and a grid vector g ₁ given by the period p _y and equation (182) based on inequalities (187) and (188). Likewise, the output grating element _{5008 has} grating vectors _g It is based on the same design principles and inequalities (191) and (192) as (2105).

Output grid 5008 has four distinct regions 5010, 5012, 5014, 5016 arranged in the x-y plane.

Regions 5010 are strips that extend along the length of output grating 5008 along the x-axis and are displaced along the y-axis with respect to input grating 5006. Region 5010 is the region that initially receives light from input grating 5006 because it is closest to input grating 5006.

Central zone 5012, also called balanced zone 5012, is located further along the y-axis than zone 5010 with respect to input grid 5006. On either side of the central region 5012 along the x-axis are regions 5016 and 5014. Regions 5016 and 5014 are in the form of rectangular strips extending along the y-axis.

Regions of output grating 5008 have different diffraction efficiencies such that the output grating provides spatially varying diffraction efficiency depending on the direction in which light propagates (along the x or y axis). The term diffraction efficiency is defined as the radiant power of a specific diffraction order (diffraction interaction) relative to the radiant power of the incident beam. The incident beam is the beam that is incident on the area of the grating (i.e. zone) that is related to the diffraction efficiency. The diffraction efficiencies of the orders (i.e., diffraction interactions) shown in Table 2 of FIG. 70 for zone 5016 and zone 5014 are the same. However, zones 5016 and 5014 have different diffraction efficiencies than zones 5010 and 5012. Likewise, zones 5010 and 5012 have different diffraction efficiencies, as described in more detail below.

A grating region with high diffraction efficiency of the STE order will provide high power coupling of the propagating light with the xy-wavevector mainly oriented in the y-direction. High-efficiency regions of the TEAT order will provide high power coupling of propagating light with xy-wavevectors primarily oriented in the x-direction. High diffraction efficiency regions of the conversion order provide a level of diffraction efficiency that converts light along a direction corresponding to the high efficiency order.

Zone 5010 can be viewed as a zone with relatively high conversion order efficiency compared to other zones. This region is referred to below as turn zone 5010. Since light initially enters transition zone 5010 from input grating 5006 and travels along the y-axis, it may be desirable to divert a portion of the light beam to reach a different region of grating 5008 that does not normally lie along the same central axis. desirable. Light with high conversion efficiency in region 5010 can be directed along the x-axis, thereby providing expansion along this direction. This is advantageous so that the light can reach a larger portion of the output grating 5008.

Zone 5012 has a diffraction efficiency that can be referred to as balanced efficiency because it can provide an output image with uniform diffraction efficiency. This is provided according to the order as described in Table 2 of Figure 70 and provides both transition order and eye order to enable uniform contribution of light throughout the eyebox. Zone 5012 results in the largest contribution of light to the eyebox.

The diffraction efficiency of zones 5016 and 5014 is tailored to help reduce rainbow artifacts from external light incident on grating 5008. These zones 5014, 5016 may be referred to as low rainbow artifact zones. These regions have a high optical order for beams of light traveling along a direction perpendicular to the external light (diffraction interactions), and low optical orders for beams of light traveling along a direction parallel to the external light (diffraction interactions). It was found that by having , the impact of rainbow artifacts on the eyebox can be greatly reduced.

DWC 5002 shown in Figure 52 is shown for use in an AR/VR headset in a side injection orientation. Specifically, this means that the input grating 5006 injects light toward the output grating 5008 at the side of the wearer's eyes (i.e., the x-axis shown in Figure 52 is the vertical direction of the wearer when standing). This is an important consideration for DWC 5002 to reduce rainbow artifacts caused by external light sources. As explained above, the biggest influence on the external lighting of an AR/VR headset is the light directly above the wearer's head, such as the sun or electric lighting. Therefore, the low rainbow artifact area can be placed according to the orientation of the DWC, for example, side injection or top down injection, to prevent interaction with light occurring above the wearer's head. Moreover, the worst-case scenario that causes rainbow artifacts in a rectangular lattice (such as an IRG) is when external light is incident on the grating 5008 at 90°, as discussed with respect to FIG. 49. Therefore, the worst case scenario that causes rainbow artifacts is when the external light follows the x-direction of DWC 5002 in a side injection orientation, as shown in Figure 52.

As mentioned above, the output grid element 5008 is an interleaved rectangular grid. The arrangement of the interleaved grid will now be described for each of the regions 5010, 5012, 5014, and 5016.

53 shows a simple unit cell 5024 representing the unit cell of an IRG in region 5010. In unit cell 5024, the lattice L1 of the IRG is slightly shifted in the positive x-direction with respect to the lattice L2 relative to its position as FSIRG, i.e. and am. Specifically, in the example shown in Figure 53, Optical structures S1 (5020) and S2 (5022) have a circular cross-section in the xy plane and are cylindrical structures with a diameter of 0.5p _x .

Figure 54 shows, for this unit cell 5024, {-1,-1} TX and {1,-1} T at the reflection for the angle of incidence on the IRG of the light beam with the xy-wavevector pointing only in the y-direction. +X conversion orders, STE and TEAT+x and It shows the change in diffraction efficiency of TEAT+x. As shown in Figure 54, the diffraction efficiency of the T+X conversion orders is the same as the TX conversion order and is much larger than the STE and TEAT orders. Accordingly, by having the arrangement of unit cells 5024 in region 5010, this region of the grating has high turn order efficiency, i.e. diffractive interactions that cause light to turn in the x and -x directions. , has low eye-order efficiency, i.e. diffractive interactions that outcouple light to the viewer. As such, zone 5010 achieves a high expansion of light along the x-axis, allowing light to reach the entire extent of output grating 5004.

The diffraction efficiency of a unit cell shown in a plot such as Figure 54 is the diffraction efficiency achieved through light incident on the region of the grating that has a particular unit cell. For example, the diffraction efficiency shown in Figure 54 is the diffraction efficiency when light is incident on the unit cell 5024. For T+x, Tx and STE, this may be incident light with a wavevector along the y-direction, while for TEAT+x and TEAT-x it is calculated as light with a transverse wavevector along the x-axis. This provides details about how a region of a grating with a particular structure diffracts, as long as the unit cells are oriented along the same direction with respect to the direction of incident light. These results can be obtained through an electromagnetic model that assumes that a particular unit cell repeats periodically over the entire infinite two-dimensional plane. In fact, this is a good model for the situation where the incident beam interacts only with the grid region consisting of the labeled unit cells.

55 shows a simple unit cell 5028 representing a unit cell of an IRG in region 5012. In unit cell 5028, the lattice L1 of the IRG is shifted in the positive x-direction with respect to the lattice L2 relative to its position as FSIRG, i.e. and am. Specifically, in the example shown in Figure 55, This shift in the x-direction is a larger amount than for unit cell 5024 shown in Figure 53. Optical structures S1 (5032) and S2 (5030) have a circular cross-section in the xy plane and are cylindrical structures with a diameter of 0.5p _x .

Figure 56 shows, for this unit cell 5024, {-1,-1} T +X conversion orders, STE and TEAT+x and Shows the change in diffraction efficiency of TEAT-x. As shown in Figure 56, the diffraction efficiency of the T+X transition order is the same as the TX transition order and the TEAT order symmetrically outcouples the light to the eye after each transition. As can be seen, the diffraction efficiency of TEAT order is greater for unit cell 5028 than for unit cell 5024. The STE order also has greater efficiency for unit cell 5028 than for unit cell 5024, but this is less important than the TEAT order.

Accordingly, by having the region 5012 formed as an IRG with unit cell 5028, this region of the grating has a relatively high conversion order efficiency, i.e., both diffractive interactions that cause the light to convert in the x and -x directions. Zone 5012 also has improved eye order efficiency, i.e. diffraction interactions that do not couple light to the viewer, compared to zone 5010. As such, zone 5012 can achieve expansion of light along the x-axis, allowing light to reach the full extent of output grating 5004 and also achieve outcoupling of light. Accordingly, zone 5012 may provide a uniform distribution of light to the eyebox.

57 shows a simple unit cell 5034 representing a unit cell of an IRG in region 5014. In unit cell 5034, the lattice L1 of the IRG is shifted in the positive y-direction with respect to the lattice L2 relative to its position as the FSIRG, i.e. and am. Specifically, in the example shown in Figure 55 am. As can be seen, this shift in the y-direction is a larger amount than the equivalent shift in the x-direction for unit cells 5024 and 5028 shown in Figures 53 and D. Optical structures S1 5036 and S2 5038 are cylindrical structures with a circular cross-section in the xy plane and a diameter of 0.6p _x , i.e., slightly larger than the optical structures of unit cell 5024 and unit cell 5034. . Shifting the IRG's lattice L1 in the positive y-direction with respect to lattice L2 causes S1 5036 and S2 5038 to overlap, as can be seen in Figure 57. In this way, S1 (5036) and S2 (5038) form a continuous structure along the x-direction. This can be called a pseudo-linear structure.

Figure 58 shows, for this unit cell 5034, {-1,-1} TX and {1,-1} T in the reflection for the angle of incidence on the IRG of the light beam with the xy-wavevector pointing only in the y-direction. +X conversion orders, STE and TEAT+x and Shows the change in diffraction efficiency of TEAT-x. As can be seen in Figure 58, the diffraction efficiency of the STE order is superior to that of other orders, while that of the TEAT order is very low. As can be seen, the diffraction efficiency of the STE order for this unit cell 5034 is much greater than the diffraction efficiency of the STE order for unit cell 5024 and unit cell 5028.

Accordingly, by having the arrangement of unit cells 5034 in region 5014, this region of the grating has a high optical order efficiency for light incident along the y-direction, whereas it has a high optical order efficiency for light incident along the x-direction. It has a low eye-order efficiency. In other words, it has a high efficiency for diffraction interaction such that light before diffraction interaction is outcoupled from a grating with an xy-wave vector pointing along the y-direction, and light before diffraction interaction is directed along the x-direction. It has a low efficiency of diffractive interactions that cause light to be outcoupled from the grating with the xy-wave vector pointing along . For the side injection arrangement shown in Figure 52 as explained above, the main cause of rainbow artifacts in the output image is external light incident on the grating along the x-direction. Having a region 5014 formed of IRG with unit cells 5034 makes it possible to reduce rainbow artifacts in the eyebox for a light beam oriented along the x-axis. However, with a high outcoupling efficiency for light with the xy-wavevector pointing along the y-axis, light originating from the input grating 5006 reaching area 5014 can still be outcoupled to the eyebox. there is. This reduces the amount of rainbow artifacts in the eyebox while ensuring that this area of the grid can still provide light to the eyebox. The term rainbow artifact is applied to a variety of phenomena in which rainbow artifacts appear.

Note that zone 5016 has the same unit cell 5034 structure as shown in Figure 57, so that the diffraction efficiency described above applies to zone 5016 as described above for zone 5014. In this way, region 5016 helps reduce rainbow artifacts in the image in the same way as region 5014. The choice to have regions 5014 and 5016 as regions of the output grating 5008 designed in this way is due to the fact that these outer regions of the grating are typically the regions that provide the largest contribution of rainbow artifacts to the output.

59 shows the TEAT order (i.e., in the It shows a direct comparison between the diffraction efficiency of incident light and low rainbow artifacts. The curve in Figure 59 is the TEAT diffraction efficiency for a light beam coming from air (i.e. external light) rather than diffracted in TIR (see Figures 56 and 58). Box 5015 represents the range of incidence angles of the source that can reach the ibox when outcoupled by the output grating. As can be seen, the low rainbow artifact zones 5014, 5016 have a much lower x-direction diffraction efficiency, so that, for example, the rainbow artifact zones 5014, 5016 are the same as the balance zone 5012. This results in lower overall unwanted rainbow artifacts in the eyebox than with a unit cell structure.

FIG. 60 shows the DWC 5002 of FIG. 52 showing the possible path of light through output grating element 5008 after being received from input grating 5006. As can be seen, the light from the input grating travels along the y direction before first diffracting at point 6002 in region 5010. Due to the high diffraction efficiency of the conversion order in region 5010, the light is converted symmetrically in the +x and -x directions through the conversion order, such that the light extends along the x-axis. Additional portions of the light from the input grating continue to propagate by the TIR into region 5012 and upon further diffractive interaction with region 5012 the light is redirected or outcoupled due to the associated diffraction efficiency of this region.

As can be seen in FIG. 60, light from input grating 5006 may reach region 5014 after undergoing two successive transition interactions with output grating elements 5008. Specifically, light is incident from input grating 5006 along the y-direction and undergoes a first transition at point 6002 to be oriented in the -x-direction, and the light beam propagates along the -x-direction by TIR. . At point 6004 after the second turn the light is again oriented along the y-direction. The light then propagates by the TIR along the +y-direction and reaches region 5014. A portion of the light at point 6006 in region 5014 may be outcoupled through the two-eye order because the xy-wavevector has a high diffraction efficiency for the two-eye order in this region 5014. This is because it is oriented only along the y-direction. Additional portions of the light continue to propagate by TIR along the +y-direction in region 5014 until outcoupled through the two-eye order at point 6008, because the xy-wavevector is in this region ( This is because it is oriented only along the y-direction, which is the direction with high diffraction efficiency for the two-eye order.

Likewise, light from input grating 5006 may reach region 5016 after two successive transition interactions with output grating elements 5008. Specifically, light is incident from input grating 5006 along the +y-direction and undergoes a first transition at point 6002 such that a portion of the light is oriented in the +x-direction, and the light is oriented in the +x-direction by TIR. It spreads accordingly. At point 6010 after the second turn the light is again oriented along the +y-direction. The light then propagates by the TIR along the +y-direction and reaches region 5016. A portion of the light at point 6012 in region 5014 may be outcoupled through the two-eye order because the xy-wavevector is in the y-direction, which is the direction of high diffraction efficiency for the two-eye order. This is because it is oriented only accordingly. Additional portions of the light continue to propagate by TIR along the +y-direction in region 5016 until they are outcoupled through the two-eye order at point 6014, because the xy-wavevector is This is because it is oriented only along the y-direction, which is the direction with high diffraction efficiency for the two-eye order.

Light in region 5012 may be diffracted into both the transition order and the optic order, as described and shown with respect to FIG. 56 . This can be seen, for example, in Figure 60, where diffraction of light at point 6016 results in an order causing a portion of the light traveling along the +y-direction to change direction and propagate along the +x axis. However, as noted above with respect to Figure 58, for light propagating along the x-axis and reaching area 5016 or 5014, there will be Designed to reduce the effects of rainbow artifacts, the low diffraction efficiency of light traveling along this axis in these regions causes most of it not to be diffracted out of these regions.

61 shows a further example DWC 6020 comprised of an optically transmissive planar substrate 6024, inside which an input grating 6022 is provided to receive projected light and couple it to a waveguide within the substrate. , there is an output grating element 6026 based on an interleaved rectangular grid and divided into multiple zones 6028 6030 6032 6034. Output grating element 6026 is a further example of an output grating element designed to reduce rainbow artifacts in the output image. The coordinate axes shown in Figure 61, like the other figures, are local waveguide coordinate axes, with the y-axis from the input grid to the output grid and the x-axis perpendicular to the y-axis. Note that, as used herein, the terms “x-axis” and “x-direction” are used interchangeably, as are the terms “y-axis” and “y-direction.”

Output grid 6026 has the same zone layout as output grid 5008, namely a high transition zone 6028, a central zone 6030, and two low rainbow artifact zones 6032, 6034. Transition zone 6028 has the same unit cell structure as zone 5010, as described for output grid 5008 and shown in FIG. 53. Central zone 6030 has the same unit cell structure as zone 5012, as described for output grid 5008 and shown in FIG. 55. In this way, the diffraction efficiency of zone 6030 is the same as zone 5012, and the diffraction efficiency of zone 6028 is the same as zone 5008.

DWC 6020, shown in Figure 61, is shown to be used in an AR/VR headset with top-down injection. Specifically, this means that the input grating injects light into the output grating 5008 above the wearer's eyes (i.e., the Y axis shown in FIG. 61 is oriented vertically when the wearer is standing, or, put another way, from the input grating to the output grating 5008). injection of light towards is perpendicular to the line intersecting the wearer's left and right eyes).

As illustrated in Figure 52 above, the orientation of DWC 6020 when in use is an important consideration as it intentionally reduces rainbow artifacts caused by external light sources. As explained above, the biggest influence on the external lighting of an AR/VR headset is the light directly above the wearer's head, such as the sun or electric lighting. Since DWC 6020 in top-down injection is effectively oriented at 90° relative to DWC 5002 when used in side injection, the worst-case scenario causing rainbow artifacts is that for DWC 6020, as shown in Figure 61, external illumination is y This is the case along the -axis (local waveguide coordinate axis). Accordingly, the low rainbow artifact regions 6032 and 6034 of the output grating 6026 have a diffraction efficiency that is different from the diffraction efficiency as described above in the regions 5014 and 5016 for the output grating 5008. This is achieved by the IRGs in the low rainbow artifact regions 6032 and 6034 having different unit cells of the IRGs as in the low rainbow artifact regions 5014 and 5016 for the output grating 5008.

62 shows a simple unit cell 6036 representing a unit cell of an IRG in region 6032. In the unit cell (curl6036), the lattice L1 of the IRG is shifted in the positive -x-direction with respect to the lattice L2 relative to its position as the FSIRG, i.e. and am. As can be seen, this shift in the -x-direction is a larger amount than the equivalent shift in the +x-direction for unit cells 5024 and 5028 shown in Figures 53 and D. Specifically, in the example shown in Figure 57, optical structures S1 (6038) and S2 (6040) are cylindrical structures with a circular cross-section in the xy plane and a diameter of 0.6p _x , i.e., unit cell 5024 and unit cell It is slightly larger than the optical structure of (5034). Shifting the IRG's lattice L1 in the -x-direction with respect to lattice L2 causes S1 (6038) and S2 (6040) to overlap, as can be seen in Figure 62. In this way, S1 (6038) and S2 (6040) form a continuous structure along the y-axis. This can be called a pseudo-linear structure.

As can be seen in FIG. 62 , the top-down injection arrangement has a lower density in regions 6032 and 6034 compared to the optical structure forming a continuous structure along the x-axis for the side injection arrangement in regions 5014 and 5016. It has an optical structure that forms a continuous structure along the y-axis. However, with respect to the external light source in question (above the wearer's head), these continuous structures have the same orientation and therefore provide the same effect of reducing the diffraction of external light into rainbow artifacts in the output image. With this particular arrangement of unit cells 6036 in regions 6032 and 6034, the diffraction efficiency of the TEAT order is dominant over each of the other orders, while the diffraction efficiency of the STE order is very low. The diffraction efficiency of TEAT order for this unit cell 5034 is much greater than that of unit cells 5024 and 5028 in zones 6030 and 6028. As can be seen in Figure 63, for this unit cell 6036, the reflection for the angle of incidence on the IRG of the light beam with the xy-wavevector pointing only in the y-direction is {-1,-1} TX and {1 ,-1} T+X conversion orders, STE and TEAT+x and Shows the change in diffraction efficiency of TEAT-x. As can be seen in Figure 63 The diffraction efficiency of the TEAT+x and {1,0} TEAT-x orders is superior to the other orders, while the STE order is very low (i.e., contrary to Figure 58).

Accordingly, by having the arrangement of unit cells 6036 in region 6032, this region of the grating has a high optical order efficiency for light incident along the x-direction, while for light incident along the y-direction It has a low eye-order efficiency. In other words, it has a high efficiency for diffraction interaction such that light before diffraction interaction is outcoupled from a grating with an xy-wave vector pointing along the x-direction, and light before diffraction interaction is directed along the y-direction. It has a low efficiency for diffractive interactions that cause light to be outcoupled from the grating with the xy-wave vector pointing along . As explained above, for the top-down injection arrangement shown in Equation 61, the main cause of rainbow artifacts in the output image is external light incident on the grating along the y-direction. Having a region 6032 formed of IRG with unit cells 6036 makes it possible to reduce rainbow artifacts in the eyebox for a light beam oriented along the y-axis. However, light originating from the input grating 6022 reaching region 6032 can still be outcoupled to the eyebox, as has a high outcoupling efficiency for light with the xy-wavevector pointing along the x-axis. there is. This reduces the amount of rainbow artifacts in the image while ensuring that this area of the grid can still provide light to the eyebox.

Note that zone 6034 has the same unit cell 6036 structure as shown in Figure 62, so the diffraction efficiency described above for zone 6032 applies to zone 6034. In this way, region 6034 helps reduce rainbow artifacts in the image in the same way as region 6032.

Although not shown, light in DWC 6020 is coupled to light out-coupled in region 5014 or 6016 of DWC 5002 for light to be coupled to the eye in region 6032 or region 6034. It will be understood that it would have traveled along a different route than that described. The path of light reaching and outcoupling from region 6032 or region 6034 from input grating 6022 need only undergo a single transition order rather than two transition orders as described for the side injection arrangement shown in FIG. do. When converted to propagate along the x-axis, light in area 6030 may be outcoupled to viewers in area 6032 and 6034. Light directed from the high transition region 6028 toward regions 6032 and 6034 has an xy-wavevector pointing along the y-direction, thereby becoming the primary path for light to be outcoupled from regions 6032 and 6034; Outcoupling efficiency is low in zones 6032 and 6034. Accordingly, the purpose of high transition zone 6028 in this arrangement is to provide expansion of light from the input grating primarily along the x-direction to reach the entire zone 6030.

FIG. 64 shows a further example DWC 6042 for use in the side injection direction described above with respect to DWC 5002 of FIG. 52 . DWC 6042 is identical to DWC 5002 except for the area of output grid 5008 where transition zone 5010 is located in output grid 5008.

DWC 6042 has an input grid 6044 and an output grid 6048. The output grid 6048 has a central region 6056 and low rainbow artifact regions 6058, 6060 that are identical (both in location and unit cell structure of the output grating) to the corresponding region of DWC 5002, as shown in Figure 52. has

The only difference between DWC (6042) and DWC (5002) is the transition area. The transition region is divided into three different regions with different unit cell structures and different diffraction efficiencies. In the output grating 6048, a central transition region 6050 extends along the length of the extremity of the central region 6056 on the x-axis closest to the input grating 6044, and the two regions 6052, 6054 are On either side of the central transition zone along the x-axis adjacent to the ends of the lower rainbow artifact zone closest to (6044). Central transition zone 6050 has the same unit cell structure as transition zone 5010 and therefore has the same diffraction efficiency as shown in Figure 58, as described above.

The purpose of zones 6052 and 6054 is to provide selective diffraction of light in these regions such that the selectivity shifts toward the low rainbow artifact zones 6058 and 6060.

65 shows a simple unit cell 6062 representing the unit cell of an IRG in region 6052. In unit cell 6062, the lattice L1 of the IRG is slightly shifted in the positive x-direction and positive y-direction with respect to the lattice L2 relative to its position as FSIRG, i.e. and am. Specifically, am. Optical structures S1 (6066) and S2 (6064) have a circular cross-section in the xy plane and are cylindrical structures with a diameter of 0.5p _x .

Figure 66 shows, for this unit cell 6062, {-1,-1} TX and {1,-1} T in the reflection for the angle of incidence on the IRG of the light beam with the xy-wavevector pointing only in the y-direction. +X conversion orders, STE and TEAT+x and Shows the change in diffraction efficiency of TEAT-x. As shown in Figure 66, the diffraction efficiency of the TX transition order is greater than that of the T+X transition order and is much larger than that of the STE and TEAT orders. Therefore, by having the arrangement of the unit cell 6062 in region 6052, this region of the grating has a high conversion order efficiency in the -x-direction, i.e., diffractive interactions that cause the light to convert in the -x direction. ,low conversion order efficiency in the +x direction, i.e. the light switches in the +x direction and has diffractive interactions providing asymmetric conversion. Likewise, this asymmetric conversion also exists for light traveling along the -x-axis, i.e., with a low conversion order efficiency in the +y-direction, i.e. diffractive interactions that cause the light to switch in the +y-direction, and in the -y-direction. has a low conversion order efficiency, i.e. diffractive interactions that cause the light to convert in the -y direction). Additionally, the eye's order efficiency is low, i.e. there are diffraction interactions that do not couple the light to the viewer. Accordingly, zone 6052 can achieve redirection of light toward zone 6058.

Figure 67 shows a simple unit cell 6068 representing the unit cell of the IRG in region 6054. In unit cell 6068, the lattice L1 of the IRG is slightly shifted in the positive x-direction and negative y-direction with respect to the lattice L2 relative to its position as FSIRG, i.e. and am. Specifically, Optical structures S1 (6072) and S2 (6070) have a circular cross-section in the xy plane and are cylindrical structures with a diameter of 0.5p _x .

Figure 68 shows, for this unit cell 6068, {-1,-1} TX and {1,-1} T at the reflection for the angle of incidence on the IRG of the light beam with the xy-wavevector pointing only in the y-direction. +X conversion orders, STE and TEAT+x and It shows the change in diffraction efficiency of TEAT+x. As shown in Figure 68, the diffraction efficiency of the T+X transition order is larger than that of the TX transition order and much larger than that of the STE and TEAT orders. Therefore, by having the arrangement of unit cells 6068 in region 6054, this region of the grating has a high conversion order efficiency in the +x-direction, i.e., diffractive interactions that cause light to convert in the +x direction. , has a low conversion order efficiency in the -x direction, i.e. the light switches in the -x direction and has diffractive interactions providing asymmetric conversion. Likewise, this asymmetric conversion also exists for light traveling along the +x-axis, i.e., with a low conversion order efficiency in the +y-direction, i.e. diffractive interactions that cause the light to switch in the +y-direction, and in the -y-direction. has a low conversion order efficiency, i.e. diffractive interactions that cause the light to convert in the -y direction). Additionally, the eye's order efficiency is low, i.e. there are diffractive interactions that do not couple the light to the viewer. Accordingly, zone 6054 can achieve selective redirection of light toward zone 6060.

Although aspects of the disclosure have been described in detail, it will be apparent that there are many other alternatives or modifications to the arrangements described above that are possible without departing from the scope of the aspects of the disclosure as defined in the appended claims.

As shown in Figures 52 and 61, the output grating element each has two zones designed to reduce rainbow artifacts in the output image. However, the output grid may contain only a single region designed to reduce rainbow artifacts. For example, output grid 5008 shown in FIG. 52 may include only region 5014, and region 5012 may extend into the grid area shown in FIG. 52 with region 5016. Alternatively, the output grid 5008 shown in FIG. 52 may include only region 5016, with region 5012 extending into the grid region shown in FIG. 52. The same modification can be applied to the top-down injection arrangement shown in Figure 61. In another arrangement, two low rainbow artifact regions may instead have different diffraction efficiencies. For example, zones 5014/6032 may have a higher diffraction efficiency for a particular order/diffraction interaction than zones 5016/6034. This can be achieved by having slightly different offsets between the grids between these areas.

An output grating that can reduce rainbow artifacts in the above description may include transition regions 5010 and 6028 that provide an initial high transition in the x-axis. However, in some arrangements this high transition zone may not exist, and the balance zone 5012, 6030 may extend into the area of the output grid where transition zones 5010, 6028 are shown in the arrangement described above.

The above example addresses a specific placement of DWC to reduce the effect of rainbow artifacts appearing along a specific direction from the light above the wearer's head. However, the invention described herein is not limited as such. The output grating may be configured to reduce light incident on the output grating in different directions. For example, the light that we want to prevent from causing rainbow artifacts may be incident on the wearer from the side rather than directly above the head. In this case the configuration of the low rainbow artifact area is adjusted appropriately to prevent light from diffracting in this direction. The purpose of the low rainbow artifact area is to reduce light coupling into the waveguide along the direction of the external light. As described above, this can be achieved through a shift of the optical structure within the unit cell of the grid forming a continuous structure along an axis perpendicular to the direction in which external light is incident. However, the efficiency of the diffractive interaction to provide outcoupling for light traveling along an axis parallel to the direction in which the external light is incident is greater than the outcoupling for light traveling along an axis perpendicular to the direction in which the external light is incident. Any structure in the low rainbow artifact region, which provides higher diffraction interaction efficiency, can serve to reduce rainbow artifacts. For example, the structure need not be continuous. For example, the circular structure shown in the example above, although having a smaller cross-sectional area in the x-y plane, may not result in a continuous structure, but can still provide the desired efficiency difference between STE and TEAT. .

The above description of the structure for low rainbow artifact DWC is not limited to the optical structure S1 S2 with circular cross-section. Any structural form described herein may be used to achieve the same effect. For example, the structure may have a cross-section that is square, rectangular, triangular, or any other shape when viewed in the xy plane as described herein. The optical structure S1 and S2 may be regions physically extending from the surface. Alternatively, the optical structure may be a hole with depth to the surrounding area.

The shifts described above are displayed for each region. However, the specific shifts indicated for each zone are specific examples of shifts that may be used. For example, in transition zone 5010 the shift is It can be within . In the balance zone (5012), shifting ranges may be in In the lower rainbow artifact area (5014 5016) the shift ranges may be in

Additionally, the cross-sectional diameter of the structure in the xy plane is not particularly limited to that shown in the example DWC described above. For example, the cross-sectional size of optical structures in the low rainbow artifact region has been shown to have larger dimensions than those in the balance and transition regions, but this is not always the case. For example, each zone may have an optical structure of the same size as each other. In other arrangements, the turn zone and balanced zone may have optical structures with different sizes. In other arrangements, the lower rainbow artifact zone may have smaller optical structures compared to the balance zone and transition zone. For example, the optical structure of the balance zone may have a cross-section in the x-y plane with a diameter of 0.3-0.7, the optical structure of the transition zone may have a cross-section of the x-y plane with a diameter of 0.3-0.7p, and the low The optical structure of the rainbow artifact zone may have a cross-section in the x-y plane with a diameter of 0.3-0.7p.

Figure 64 shows two regions 6052 and 6054 providing asymmetric diffraction of transition order. Unit cells of the IRG in these regions are shown to have shifts in both the x- and y-directions (i.e. and and, i.e. and am). In another arrangement, the unit cells of transition zones 5010 and 6028 vary gradually across the x-direction to achieve the same effect as zones 6052 and 6054, rather than having zones with hard boundaries. . Alternatively or additionally, the size of the optical structure in the xy-plane can be varied across the transition region to achieve the effect of regions 5010 and 6028 as shown in Figure 40H.

Each zone shown in Figures 52, 61 and 64 is shown as having boundaries in a different arrangement, but changes between zones may be gradual. For example, as shown in Figure 40h. Additionally, the shape and dimensions of the zones are not limited to those shown in the drawings and described above.

Claims (15)

In a waveguide for use in virtual reality, VR or augmented reality, AR devices,
an input region configured to couple light to the waveguide to propagate under total reflection (TIR) within the waveguide; and
An output region comprising an optical structure configured to receive image bearing light from the input region in a direction along a first axis, the output region comprising a first diffractive interaction that outcouples light propagating along the first axis to a viewer. , a second diffractive interaction that outcouples light propagating along a second axis perpendicular to the first axis to the viewer, and a third diffractive interaction propagating under the TIR in the waveguide along an axis perpendicular to the axis before propagating. providing a diffractive interaction for light propagating under TIR in said waveguide, including a third diffractive interaction that converts the light such that -
Including,
The output area is,
a plurality of zones each having different non-zero diffraction efficiencies for the first, second, and third diffraction interactions
Including,
The plurality of zones are,
Zone 1, and
a second zone located at a position along the second axis relative to the first zone
Including,
The diffraction efficiency of the first diffractive interaction in the second zone is:
greater than the diffraction efficiency of the second diffractive interaction in the second zone and greater than the diffraction efficiency of the first diffractive interaction in the first zone, thereby reducing rainbow artifacts;
or
The diffraction efficiency of the second diffractive interaction in the second zone is:
greater than the diffraction efficiency of the first diffractive interaction in the second zone and greater than the diffraction efficiency of the second diffractive interaction in the first zone, thereby reducing rainbow artifacts.
wave-guide.
According to paragraph 1,
When the second zone has a diffraction efficiency of the first diffractive interaction that is greater than the diffraction efficiency of the first diffractive interaction of the first zone,
The second zone may have a diffraction efficiency of the second diffraction interaction that is less than the diffraction efficiency of the second diffraction interaction of the first zone, or
When the second zone has a diffraction efficiency of the second diffraction interaction that is greater than the diffraction efficiency of the first diffraction interaction of the second zone,
The second zone may have a diffraction efficiency of the first diffraction interaction that is less than the diffraction efficiency of the first diffraction interaction of the first zone,
wave-guide.
According to any one of claims 1 and 2,
When the second zone has a diffraction efficiency of the first diffraction interaction that is greater than the diffraction efficiency of the second diffraction interaction of the second zone,
the second zone comprises a continuous optical structure along the second axis, or
When the second zone has a diffraction efficiency of the second diffraction interaction that is greater than the diffraction efficiency of the first diffraction interaction of the second zone,
the second zone comprising a continuous optical structure along the first axis,
wave-guide.
According to any one of claims 1 to 3,
Each area,
a first rectangular periodic optical structure array disposed in a plane defined by the first axis and the second axis,
a second rectangular periodic optical structure array disposed on the plane
Including,
The period of the first rectangular array is,
defined by the spacing between neighboring optical structures of the first rectangular array,
The first rectangular periodic array is:
forming a first 2D lattice with rectangular symmetry,
The period of the second rectangular array is,
defined by the spacing between neighboring optical structures of the second rectangular array,
The second rectangular periodic array is:
forming a second 2D lattice with rectangular symmetry,
The first rectangular optical structure array,
superimposed on the second rectangular optical structure array in the plane such that the arrays are spatially offset from each other in the plane;
The first optical structure array is,
offset from the second array of optical structures by a factor different from half a period of the first or second rectangular array.
wave-guide.
According to paragraph 4,
When the second zone has a diffraction efficiency of the first diffraction interaction that is greater than the diffraction efficiency of the second diffraction interaction of the second zone,
The second zone is,
the first or second rectangular array such that the first array of optical structures differs from the period of the first or second rectangular arrangement and the optical structures of the first and second arrays form a continuous structure along the second axis. comprising first and second arrays of optical structures positioned to be offset from the array of second optical structures in the first axis by a factor different from half the period of the array;
or
When the second zone has a diffraction efficiency of the second diffraction interaction that is greater than the diffraction efficiency of the first diffraction interaction of the second zone,
The second zone is,
The first or second array of optical structures is different from the period of the first or second rectangular arrangement and the optical structures of the first and second arrays form a continuous structure along the first axis. comprising first and second arrays of optical structures positioned to be offset from the array of second optical structures in the second axis by a factor different from half a period of the array.
wave-guide.
According to clause 4 or 5,
The first zone is,
An optical structure arranged such that the first array of optical structures is offset from the second array of optical structures by a factor different from half the period of the first or second rectangular array along the second axis.
Includes, and
The first optical structure array is,
offset from the second array of optical structures by half a period of the first or second rectangular array along the first axis.
wave-guide.
According to any one of claims 1 to 6,
A third zone receiving light directly from the input area
It further includes,
The third zone is,
having a diffraction efficiency of the third diffraction interaction that is higher than the diffraction efficiency of both the first and second diffraction interactions of the third zone, and
The third zone is,
located at a position along the first axis relative to the first zone, and
The first zone is,
having a diffraction efficiency of the second diffraction interaction that is greater than the diffraction efficiency of the second diffraction interaction of the third zone,
wave-guide.
In clause 7,
When the diffraction efficiency of the first diffraction interaction in the second zone is greater than the diffraction efficiency of the first diffraction interaction in the first zone,
the diffraction efficiency of the first diffractive interaction in the second zone is also greater than the diffraction efficiency of the first diffractive interaction in the third zone, and
When the diffraction efficiency of the second diffraction interaction in the second zone is greater than the diffraction efficiency of the second diffraction interaction in the first zone,
the diffraction efficiency of the second diffractive interaction in the second zone is also greater than the diffraction efficiency of the second diffractive interaction in the third zone,
wave-guide.
According to clause 7 or 8,
Pursuant to paragraph 4, paragraph 5 or paragraph 6,
The third zone is,
An optical structure arranged such that the first array of optical structures is offset from the second array of optical structures by a factor different from half the period of the first or second rectangular array along the second axis.
Includes, and
The first optical structure array is,
offset from the second array of optical structures by half a period of the first or second rectangular array along the first axis.
wave-guide.
According to clause 9,
The factor by which the first array of optical structures is offset from the second array of optical structures along the second axis in the third zone is:
less than a factor by which the first array of optical structures is offset from the second array of optical structures along the second axis in the first region,
wave-guide.
According to any one of claims 1 to 10,
The optical structure of the second zone is,
each having a cross-sectional area in a plane defined by the first and second axes that is greater than a cross-sectional area of the optical structure in the first zone,
wave-guide.
According to any one of claims 1 to 11,
The input area is,
A 1D linear grid,
wave-guide.
According to any one of claims 1 to 12,
a fourth zone positioned at a location along the second axis relative to the first zone and along the first axis relative to the second zone
It further includes,
The fourth zone is,
diffracting light primarily through the third diffractive interaction to selectively divert the light toward the second zone along the first axis.
wave-guide.
According to any one of claims 1 to 13,
further comprising a fifth district;
The fifth zone is,
Has the same diffraction efficiency as the second zone,
disposed at a position opposite the first zone relative to the second zone along the second axis,
wave-guide.
Augmented reality or virtual reality display comprising a waveguide according to any one of claims 1 to 14.